Hiya!
[MENTION=6880599]ClaytonCross[/MENTION], I'm going to have to say...no? I've played a LOT of RPG's over the years. Most of the longer ones tend to be Fantasy, followed by Gamma World (3rd Edition; I would have said 'Apocalyptic', but honestly, the only real Apocalyptic we play consistently...at least up until about a year ago...was 3rd edition Gamma World), then Super-Heroes. Everything else falls after that. Of the Fantasy, a LOT of it has been either 1e/Hackmaster, BECMI/DarkDungeons (
https://darkdungeonsblog.wordpress.com/), Powers & Perils (
www.powersandperils.com), or Dominion Rules (
www.dominionrules.org).
Anyway, I've been trying to think back to almost 40 years of DM'ing some form of "D&D" and I think I can honestly say, only my first 5 to 10 years of DM'ing was 'stuff' a common motivator. After about a decade I sort of hit my stride/style for DM'ing and I think I've remained fairly consistent over the decades...with only a slight mellowing on the whole 'detailed rules' side of it all (old age and all that I guess!

).
Talking specifically about the last 15 to 20 years, I can tell you that my Players main "goal" and driving force behind their PC's is "Try not to die!". I'm what is termed, nowadays at least, a "Killer DM". My players also call me 'stingy on the side of treasure'. I attest affirmative to both those things. The highest level PC anyone has had in my 5e campaign(s) was: 7th level Goliath Barbarian, 5th level Tiefling Bard, 4th level Human Thief, 4th level Human Druid. After that, it's a handful of 3rds, about twice that in 2nd, and twice that again in 1st level characters. This is over about 4 years I guess? Whenever the Starter Set came out.
My point is...no, IME. If you present a game where other things simply ARE more important (survival; and that usually goes hand in hand with cautious play, development of NPC ties, and story-goals a Player develops based not on 'stuff to acquire'), then "getting tougher" is a nice sideline bonus. In my campaigns saving a town, country or entire world is simply not dependant on "level" or "power". My campaign (and DM'ing style) is most definitely an "outlier" of the modern RPG expectation of play. I get that. It's cool with me and my group.
^_^
Paul L. Ming