To start with, if the game itself fails to dissuade the player from taking every item in every room then not doing so should only be a factor of the player's available time. If you want to "play a character" who doesn't steal, but the game never ever punishes you from picking up items in people's homes, then it's bad game design that fails to accommodate that particular play style. On the other hand, there have been loads of CRPGs in the history of the genre that punish you for stealing items. Many of them have NPCs that sound alarms or turn hostile, others reduce virtue or karma scores. Some reduce your reputation with various factions, while some have strict time limits that discourage searching through every single container.
Another point to make, specifically with Deus Ex, is that eliminating all those lootable items hidden away in containers will reduce the use of the lock picking and electronic skills. One of the key benefits of those skills is to reduce the amount of lock picks and multi-tools required to break in to places. Sure, they can still be useful during the non-optional parts of missions, but the game makes a point to supply you with alternatives so that you don't ever have to use them. And not only that, there's plenty of lock picks and multi-tools around to last you through the "vital" sections of the game. It's when you dive into those optional areas for loot that the electronic and lock picking skills become useful and beneficial.
On the topic of "leveling up", no, you don't need to strictly level up in an RPG. However, you do need to be able to define your character in another way, ordinarily through a character creator at the start of the game. The problem with this method is that the player can't learn the usefulness of various attributes and skills and adapt their character accordingly without restarting the game. Leveling up provides the means to learn about the game and grow a character in a decent way. Of course, in a perfect game where every skill is useful and every combination of skills results in a valid play style, a pure character creator system without leveling up would be just as good from both an RPG perspective and the player's perspective. However, no game has come close to this and so having leveling up is the best we can hope for right now.
You did mention something about getting experience for doing things the hard way, and I agree with you that this sucks. You should be rewarded similarly for killing everyone, playing diplomatically, and stealthing through a level. I'm all in favour of rewards for different play styles. Perhaps even different rewards catered to those play styles. Completing a quest in a stealthy way will reward you with a something useful for stealthy characters etc. Deus Ex's system of rewarding skill points for exploration is pretty bad if you ask me. Probably the worst aspect of the entire game.