I use the Variant: Spell Points system frequently at my table.
What happened is that my sorcerer players use their resources more consistently, before they often forgot to convert low-level spell slots to Sorcery Points. It leads to less frustration once the initial set-up is done, and streamlines resource accounting - it became uniform and easier. My players feel empowered and informed. As a GM it is much easier to keep track of the expended resources because you can easily subtract Spell points from one uniform number without keeping track of Spell slot levels.
The only balance issue that we came across is that you don't as frequently use your bonus action for
Converting a Spell Slot to Sorcery Points. (PHB 101):
As a bonus action on your turn, you can expend one spell slot and gain
a number of sorcery points equal to the slot’s level.
So my sorcerers are more efficient now, and they use the Sorcery points to their advantage. Instead of having to spent 4 turn's bonus actions on converting low level spell slots, they can convert an amount of Spell points to Sorcery points in one bonus action (in one round).
The issue stems from this part of the optional rule, my emphasis:
Instead of gaining a number of spell slots to cast your spells from the
Spellcasting feature, you gain a pool of spell points instead. You
expend a number of spell points to create a spell slot of a given
level, and then us that slot to cast a spell.
So you can create a spell slot of any level that is available to you to convert it into Sorcery Points instead of converting the spell slots that would normally be available to you.
In particular, they are more efficient while using the metamagic Quickened Spell: (PHB 102)
When you cast a spell that has a casting time of 1 action, you can
spend 2 sorcery points to change the casting time to 1 bonus action
for this casting.
The amount of options increases and it especially matters when you have a low amount of spell slots of a particular level, that is commonly one additional Cantrip cast if available via Bonus Action (PHB 202):
A spell cast with a bonus action is especially swift. You must use a
bonus action on your turn to cast the spell, provided that you haven’t
already taken a bonus action this turn. You can’t cast another spell
during the same turn, except for a cantrip with a casting time of 1
So at my table when using the Variant: Spell Points system my players are slightly stronger, but they also have more fun and feel like the game is less complicated.
I can speculate that the impact on balance would increase if your players multi-class and get impactful bonus action options through class-features such as Cunning Action (PHB 96):
Starting at 2nd level, your quick thinking and agility allow you to
move and act quickly. You can take a bonus action on each of your
turns in combat. This action can be used only to take the Dash,
Disengage, or Hide action.
This case, however, has not happened at my table and all other bonus actions my players gained through multi-classing were not more impactful than the occasional additional cast of a cantrip.
Another interesting interaction that you may want to keep in mind for mulit-classing is that the Warlock's Spell Slots (107):
The Warlock table shows how many spell slots you have. The table also
shows what the level of those slots is; all of your spell slots are
the same level. To cast one of your warlock spells of 1st level or
higher, you must expend a spell slot.
are of the same level.
This optional rule is not intended for Warlocks, because they don't have a spellcasting feature (they only have a spellcasting ability) (PHB 107), this is a multi-classing annotation that could have ramifications that I have not yet seen in a game.
This answer explores how you could use Spell Points as a Warlock.