Alright, this is going to delve into both canon and conjecture, as it must for such a nebulous topic. I'll break them down so we know which is which.
The Many Gods of the Dead
As has been noted (correctly), the Wall of the Faithless was established by Myrkul. His successor Cyric kept the Wall erected largely out of malice and sadism, never questioning its existence as long as it served as a means to issue torment and suffering. With Cyric's fall, Kelemvor ascended to the portfolio of the dead and struck down the Wall, intending to enact a more "fair" accounting of the Faithless. Events shortly after his ascension led him to reconsider, and the Wall was restored.
Of course, Myrkul was not the first God of the Dead in Faerun - that honor goes to Jergal, an incredibly ancient power from the earliest days of the world. Jergal's reign preceded the Wall of the Faithless, and no cognate to it has ever been described as existing during his long tenure.
Of Power and Position
We know for a fact that Jergal was powerful, immensely so; few gods have had anywhere near the status once possessed by the original god of the dead. At the time of his voluntary abdication, Jergal was known and feared as Lord of the End of Everything, a god whose vast portfolio encompassed all that was terrible and dire. When he split apart his power and his portfolio and divided it between the Dark Three (Bane, Bhall and Myrkul), what was there was sufficient to create two greater deities and one intermediate deity, while still leaving sufficient divinity and power for Jergal to remain a demigod.
Conjectural: It is likely that, considering this immense breadth of power, Jergal never needed a Wall of anything at all. Nothing would dare cross the Lord of the End of Everything; indeed, the Dark Three might not even have dared, were Jergal himself not secretly aiding in their ambitions.
Conjectural: Conversely, at the time of his ascension Myrkul was an upstart among the gods, a mere human up-jumped to greater godhood with a major portfolio, descended from immigrated slaves, no less. Newly catapulted to the ranks of the greatest deities of Faerun and with a difficult portfolio to manage, Myrkul may well have erected the Wall both for practical reasons and also to establish his name alongside the fear of the grave.
The Value of Faith
There are two kinds of souls that require judgment by Kelemvor: the False and the Faithless. One question when disputing the morality of the Wall is why the False (active betrayers) receive variable sentences while the Faithless (which may include the spiritually apathetic) are universally condemned to the slow, torturous transition to becoming one with the Fugue Plain. The other question of morality is why any condemnation is needed at all; while Myrkul and Cyric were gods of great evil and thrived on suffering, Kelemvor is neutral and ostensibly not a fan of punishment for its own sake. How, then, can this continue?
A logical response is that the gods of the Realms require worship - and not just worship, but the souls of their faithful. The gods cannot simply lap up the belief of their living followers and then abandon them to the eternal gray of Kelemvor's domain when their mortal coils have been shuffled off - the eventual reward of the faithful soul, necessary for gods to survive, is to become part of one's patron deity. This is not a one-sided arrangement - gods are not static beings, but evolve with their worshipers. The faithful are not doomed to become the fingernails or the eyelashes of the divine, but rather gifted with the opportunity to be part of a divine renewal, transformation and maturation. This was the requirement of Ao, who punished the gods for their petty squabbles by forcing them to rely on mortals for their very survival.
In turn, the gods of Faerun have a role to play in keeping the world in order - their very existence helps maintain the forces listed in their portfolios. When a god's power is shaken, the state of Faerun can be radically warped - consider Tymora and Beshaba, whose mere weakening was enough for luck and misfortune to fly into havoc across the realms. To starve the gods of faith is to imperil one's own world and life, and the gods don't actually have a say in preventing that from happening.
All of this means that the gods have a massive incentive to not abandon souls to Faithlessness, and do what they can to claim both those souls that clearly belong to them as well as souls that might be argued to in principle be aligned to a particular god. Of course, Kelemvor must judge whether or not this is actually the case.
The question remains: why put them into the Wall at all? Jergal didn't, and it's not like the False go there. What's the point, besides needless suffering and an existential threat warning Faerunians to worship or else?
Conjectural: At the time Jergal reigned, the overall population of Faerun was likely considerably smaller. He may have had far fewer Faithless to deal with. As before, it is also noteworthy that no god of the dead has ever matched the power of Jergal - Cyric approached it, but as a noted sadist and later madman, would never have evaluated the need for the Wall during his tenure.
We know the following truths about the state of affairs in the Fugue Plain: devils are permitted to tempt souls to join them in the Nine Hells, while demons frequently raid the City and the Wall to rip souls away and carry them back to the Abyss.
Conjectural: Whereas the False built a spiritual connection in life and severed it at some point (a "broken link in a chain," if you will), the Faithless managed nothing of the kind. The result: they form, in effect, a sort of "spiritual garbage" whose presence on the Fugue Plain would be without end. No god could bring them to a deserving afterlife, for to do so a god needs to have a connection to the soul, so they must eternally remain on the Plain. After a length of time observing other souls arriving and being invited off to their eternal reward, it is likely that the spiritual turmoil that these Faithless would suffer would result in them becoming hollow shades driven by envy, not unlike undead, and lashing out at new arrivals and the servants of the god of the dead alike.
Conjectural: Following from this point, while the Faithless as souls have no right to an afterlife, they remain souls, with all the myriad applications thereof. While a god the likes of Jergal would have little trouble keeping his borders closed via threat of reprisal, for an upstart ascended human - and remember, every god of the dead since Myrkul has been an ascended human - keeping demons, night hags and dark gods from raiding the Fugue Plain and making off with loose Faithless to use in dire and unpleasant fashion would be a thankless and constant job, one with an inevitable margin of failure. Even with the Wall in place to bind the Faithless and protect the City proper, demonic raids still manage to claim a few victims every time. The existence of the Wall merely ties the Faithless more strongly to the Fugue Plain while at the same time making use of their nature to help protect and stabilize the realm for those whose souls have elsewhere to be.
But What About The False?
Conjectural: The False, as noted above, developed spiritual connections during their lifetime. The fact that one end is frayed does not change the fact that their souls have demonstrated and established the capacity for spiritual connection, which is exactly why Kelemvor takes them in and either binds them for punishment or sets them to work - and why they can work: their spiritual connection exists to give them a tether, but sans terminus they have no final reward. If they are fit to serve, they will serve, unchanged by the realm of the dead but altered for service by its lord. If they are doomed to be punished for their crimes, they will not escape, for the realm of the dead will not have them.
Conjectural: Conversely, the Faithless have no connection whatsoever - except to the realm of the dead via the property of being dead. Without a suitable tether, there is nothing for them but the Fugue Plain - they cannot exist elsewhere as whole and healthy souls, and cannot be bound to anything for they have no tether with which to hold them, so service is not a realistic option most of the time.
The (Not-So) Great Reversal (a.k.a. Kelemvor, You Jerk)
Which leads us to the current god of the dead, who took down the Wall and gave the Faithless more individualized judgments only to put it back up a short time later and restore those once bound to it to their places. What gives?
Canonically, the disassembling of the Wall was part of Kelemvor's effort to be a different kind of netherworld deity - a caring psychopomp who promised a just reward to any and all who were judged at his hand, even those who did not contribute through spiritual development to the maintenance of Faerun's balance via connection to its deities. A very human perspective, to be sure - and one that backfired horribly, as mortals catching wind of the death god's compassion entrusted themselves to his judgment and abandoned faith in their gods. With goodly souls promised a netherworld of joy and plenty and wicked souls promised torments and bitterness, Kelemvor's compassion did not merely imperil faith - it resulted in a much higher proportion of good-aligned mortals cashing in their chips, while evil-aligned mortals played it as safe as they could and as faithful as they were able, to keep out of the "kindly" death god's judgmental grasp. Kelemvor had managed to establish an eternal afterlife of contentment without spiritual fulfillment, a situation which had it escalated would have threatened the cosmos of Faerun and its pantheon.
So the Wall went back up, the Crystal Spire was dulled, and the City went from a realm of just rewards to... just a realm, re-warded. Kelemvor abandoned his humanity and compassion, striving to be fair, transparent and understandable - a better face for death than mad Cyric, cruel Myrkul or dread Jergal, but no longer one tarnished by promises of happiness without purpose or meaning for those who lived a good life and suffering without hope or mercy for those whose lives were ill-spent.
Semi-conjectural: The Faithless are not able to proceed to any afterlife other than the Fugue Plain. The gods have maximum incentive to ensure that as few souls end up Faithless as possible, through efforts both in life - evangelizing - and in death - arguing for the spiritual accord of a soul with themselves. Individuals have maximum incentive to contribute faith to the cosmos, as belief ultimately protects and sustains Faerun itself. If left on the Fugue Plain or brought into the City, the Faithless would fester into spiritual parasites, creatures of envy and fury, or else attract the attentions and belligerence of avaricious and malevolent entities who would think nothing of bringing war to the doors of death itself in order to pillage loose souls to put to use in hideous and likely destructive ways. The collateral damage from such raids would encompass souls that had earned another afterlife. Instead, the Faithless are put to use protecting the existing order, bound in a state that prevents them from getting loose and going rogue and slowly attunes them to the only spiritual destination their soul is compatible with - the Fugue Plain itself.