Four forces conspire against this: Malthus, Lebensraum, Tainter, and the idea of "dead-man's shoes"
This answer is positioned from a point of system-pragmatism, due to the "answer" is that non-combat resurrection violates many of the genre tenets (see also: using Phoenix Downs on Aerith). Assuming that we don't care about violating genre, then we have to set many of the genre conventions aside and look at the tools the system offers us. Thus, our world (like that envisioned by the econonomicon) accepts the spells and abilities presented in the mechanics of the game as given and asks "what sort of world would result?"
Before getting into said mechanics, three answers spring to mind:
- Dark sun
- Elizabeth Moon's Herris Serrano novels
- The blood war.
The dark sun series has its iconic "defiliers." A arcane caster's ultimate goal in that universe is to consume enough power to become an immortal sorcerer-king. Thus, in a world with very scarce resources, the elite become immortal god-kings and send the rest of the world into grinding subsistence level poverty.
Malthus posited that (roughly paraphrased) as the carrying capacity of the land increased linearly, and that the population of the land increased geometrically, bad things will happen:
The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.
Given scarce resources (which... is not necessarily a given in D&D, but we'll get to that later), and immortals driving population growth (if kings can do it, lords want to do it. When lords can do it, knights want to do it. ... and so on) a Malthusian crisis will be reached sooner rather than later.
The need to prevent overpopulation in a given kingdom, will inevitably lead to growth. Here, we face the ideas of lebensraum, and Tainer's catasrophies. For an absolutely fantastic treatment of this in fiction, I recommend the Herris Serrano series by Elizabeth Moon (especially the latter books) where the friction of immortality among the elite leads to... consequences.
Kingdoms will expand until they can expand no further, shedding plenty of commoner blood in the process. The horrible thought is: there is no difference between success or failure. In the case of failure, the kingdom dies. In the case of success, the kingdom pushes up against natural boundaries, becomes overpopulated, and dies. It is this inexorable requirement for growth (as the positions at the top aren't going away, but the population's sex drive isn't either, requiring that a canny elite create positions of power for ambitious youngsters to achieve over there.).
In order to combat the inexorable need for lebensraum created by population pressure (and ennui), we are faced with the final two forces: Joesph Tainter's social complexity theory and venting the ambitions of the ambitious.
Tainter posited that:
According to Tainter's Collapse of Complex Societies, societies become more complex as they try to solve problems. Social complexity can be recognized by numerous differentiated and specialised social and economic roles and many mechanisms through which they are coordinated, and by reliance on symbolic and abstract communication, and the existence of a class of information producers and analysts who are not involved in primary resource production. Such complexity requires a substantial "energy" subsidy (meaning the consumption of resources, or other forms of wealth).
By definition, societies with immortals at the top will be expansionist (or lotus-eaters, but we don't have the critical requisites for that sort of immortality in D&D). Successful societies will continue to have an absolutely atrocious gini coefficient due to the concentration of both cunning and power in those who have achieved immortality. For a terrifying look at the consequences of this line, take a look at Doc Smith's Eddorians (who handle immortality through division and then competing with their remaining selves in an endless lust for power.) The same series holds a (boring) counter example of the Arisians, themselves immortal but, as they are focused on exploring the mind, have no expansionistic tendencies.
Therefore, for the sorts of societies allowed by the mechanics of D&D, they will look rather more like Eddorians than Arisians, simply because if they looked like Arisians, there'd be nothing to actually do.
A non-immortal society will suffer proportionally higher breakdown of its complex institutions as their leaders die. This leads to change and the possibility for the non-catastrophic and local decrease in complexity as new organisations "eat the lunches" of the old, stodgy ones. With immortals with a high gini coefficient, that sort of in-built entropy will be sat upon until catastrophic collapse (See: Taleb's Black Swan of Cairo on risk suppression).
Thus, immortals will want their children to go over there and conquer. Which will work for a limited time until either the communication channels break down, overpopulation hits natural barriers, or the blood war spills over.
There is actually an example of an endlessly expanding immortal society in D&D. There are two: the demons and the devils. Both spawn endlessly, both have a very human lust for power, an infinite area to spawn in, and both have ambitious young. Thus, because they're not facing population pressure (due to that lovely idea of an infinite plane), they are facing generational pressure as the younger generations want the positions of the older. (Hence the term dead man's shoes. See "Dead wizard's pointy shoes" for a humorous treatment of the idea).
Therefore, be careful with this idea, if taken to its logical conclusion, the world wouldn't be a very nice place.
Still, that leaves the mechanics.
The most sustainable and affordable mechanism is the Last Breath spell (druid 4, for our purposes cast by a 7th level archivist to avoid any "natural" or "deific" condemnation) (Spell Compendium, p130) which:
Last breath restores life to a recently deceased creature, creating a new body for the returning spirit to inhabit. However, the spell must be cast within 1 round of the victim's death. This spell functions like reincarnate (PH 270), except that the reincarnated creature receives no level loss, no Constitution loss, and no loss of spells. The creature has -1 hit points (but is stable).
neatly avoids any losses whatsoever so long as death can be arranged easily.
This can be incorporated into a Magic Trap without too much difficulty, costing a tidy 64000gp. If I wanted to be evil about it, I'd incorporate liquid pain (BoVD) generation into the trap along with appropriate memory blocks such that the youthful person coming out the other end would have a few tidy vials of crafting xp. Setting that aside and merely presuming an honourable guillotine (call it 6 grand for the guillotine) we get an infinite use death-trap of eternal youth. At 70 grand, it's quite achievable for a number of budgets, especially as its cost can be amortised over a number of uses. One of these traps could trivially lead to an immortal nobility (saving assassination and other unfortunate ends) with the only pre-requisite being access to the device.
With this immortal nobility, we have all of the necessary pre-requisites for a Malthusian collapse. Happily, strategically positioned magic traps of Create Food and Water (and prestidigitation to reflavour the food) neatly solve many logistical problems as well as agrarian problems, allowing the entire society (save for that subset of farmers producing "luxury food" to get along with other business.) Magic traps of Wall of Iron and Wall of Fire neatly produce infinite workable metal (if not particularly good iron, there will be plenty of it. Carbon is easy enough to come by, leading to the arbitrary production of steel.)
Therefore, this immortal elite's best use of the population is as soldiers (as crafting will be recruited by the immortal elite and turned into a part of the ruling class, there will be few, expert, immortal artisans overseeing massive assembly lines (sufficient commoners with aid another can do remarkable things to epic craft checks) churning out war materiel for the "young" immortals to use when conquering.
To answer your question: rulers that have themselves resurrected efficiently lead to world-spanning empires that die and leave behind remarkably well-stocked ruins for future adventurers to discover.
Or (as I have been reminded) you effectively get a galaxy (or solar system) of endlessly respawning people flying around space swapping bodies and fighting elder horrors. In that instance, go play eclipse phase.
I have also been reminded in offsite discussion that stable fictional societies do exist with immortal kings, The goa'uld and their sarcophagi closely mimic the guillotine of eternal youth (for practical purposes, at least).
To quote my friend:
Mechanically, the key is that the magic trap only avoids natural death, and the magic trap is in the "can't be bought with money" level of expense described in the Economicon. Unnatural death by people who don't want you to come back is still a threat, particularly in the context of taking-over-or-dismantling-the-empire. If people show up, kill your servants, and disintegrate you, you're mostly staying dead. Even if you come back somehow you probably no longer have access to your magic trap of I'm-not-dead-yet.
The non-mechanical key is a social and cultural structure where only the ruling class has access to immortality /and everyone else thinks this is perfectly right and proper/. Admittedly, this requires rather particular history and cultural development, but it's not implausible.
I would only add to that the other requirement is nigh-infinite habitable planets such that the (much slower, due to smaller immortal population) expansion is not contained by natural barriers.