I want to do that because I'm virtually never motivated by wealth or items as a player, so I want to see what that's like. I play with two players who darn near killed me because I didn't understand that one of their prime motivations is loot. (I mustered the votes to trade it in for plot points. Oh, were they peeved!)
And before joining that online group, my previous campaign had me as a sorcerer in a game where we didn't evenly divide stuff,just took what we needed each and generally kept anything that could be useful later on. My sorcerer didn't need much other than +casting stat and some wands and metamagic rods. Midway through the game, the DM did a gear check on us to see if he was keeping par for the treasure value he wanted us to have. My character had less than a third the gear (in gp) than the party Fighter. Of course, by then I was a high level spellcaster, so I was more powerful than the Fighter despite that.
But yeah, I usually am motivated by loot in games. Rarely it's actual love of money on the character's part. More often, it's just the fact that wealth is the only other power axis. I just view things in a relative sense. I don't think, "we're level 5, so we're weak." I think, "we have 1.5x the expected treasure for level 5, so we're really strong!" from a power gaming perspective, it's silly to focus on levelling. The basic assumptions of the CR system and xp handouts are based entirely on what level you are. The encounters you face, and in some cases even the world around you, folds to meet roughly the party's experience level and be suitably challenging, so gaining power by levels is like paddling upstream. On the other hand, wealth plays no role in this, so if you can vastly exceed your expected wealth, then without appropriate DM adjustments, the game just plain gets easier. A level 10 party w/ expected wealth may be more powerful than a level 5 party rolling in gp when compared directly, but the PCs in the level 5 party will
feel more powerful. And since it's a game and not reality, I'd rather put my stock in feeling awesome, even if an ancient red dragon could still kill me in seconds.
I think controlling the gp-xp ratio is very important for DMs to do, I'll even dare say much more important than controlling the rate of level gain. Right now I'm running a purposely high-powered game and let the party generally end up with more money than they should have. Next campaign, I want to run a low level, low magic, gritty game, and will likely keep wealth sub-standard to further reinforce the feeling of being underpowered and struggle to survive.
EDIT:
A good defense of the entrepreneurial spirit! I would LOVE to play an aristocrat who got additional lands, wealth, and influence rather than individual superpowers as he leveled.
I forgot to add, I've actually long considered doing something like this with the aristocrat class. Every level you take in the class would cause you to gain a large amount of money -- inheritance, investments, whatever -- as a counter-balance to the no class features thing. I'd even consider an overwhelmingly large amount of money (enough for the character to, combined with regular loot gains, to have ~double or triple the normal wealth expected) if such gains were restricted to mostly non-combat, "status," property, employment, etc... kinds of things. I'd allow it to be spent on masterwork items ("only the finest will do"), but not magic items. Such a character could end up with a castle, vast estate, exquisite art galleria, an army of a wait-staff, etc... but in terms of in-combat power would not gain much benefit over a regular PC. Probably be weaker, what with the aristocrat levels and all...
The idea originally came from AE's Wealthy talent. I have tentative houserules now that any PC taking level 1 in aristocrat can have a title and legitimately be a part of the nobility, and around level 5-8 gains an inheritance similar to the second benefit of the AE feat, but have considered just going with the "wealth IS your class feature!" idea instead.
