Not using a skill system is a return to role-playing. Instead of an abstracted accounting of certain specificities in the game (or worse, no accounting whatsoever), you actually do the things you are attempting. For example, in general your character is as good at finding and disarming traps as he is at fighting monsters. He doesn't do either, you do. In other words he may have a bonus or two, but the non-combat increases are (with one notable exception) separated from class leveling. This traditional method, the role-play method, is the testing of the Player's ability through playing the world. It's the same thing you are doing when you are fighting instead of rolling an either/or percentage to see who won.
D&D used static rolls for most non-combat interactions with usually only ability scores, race and class affecting certain bonuses (i.e. Elfs finding doors, Rangers gaining surprise). However, success was rarely about these little bonuses. Truly improving the odds could really only be done by Players improving their own play, not by adding bonuses to the characters. This means a 3 in an ability score was absolutely playable though your character was somewhat worse off than others odds-wise. Ability scores simply didn't affect many things. Most rolls were the same odds for everyone regardless of ability scores or class level. Just as with combat where fighters were better, but everyone else could fight fairly well too, most actions were generally even odds across the board.
The obvious exception was the Thief. His fighting and magic using abilities were next to nil, so he was almost always played as "out of the action" when it came to combat. But in return he pretty much ruled whenever it came to doing anything else in a dungeon: sneaking around, unlocking safes, climbing walls, discerning noises, disarming traps, etc. He pretty much stole everyone else's thunder as all the other PCs attempted these actions without bonuses. (though the thief's advancement was slowed into percentile points vs. 16 2/3rds class bonuses for other classes' d6 rolls)
Of course some folks did house rule advancement into the game for certain activities via training, but these actions were not designer defined. They could just as easily be farming as hiding in shadows. But as some activities more or less related to combat it's probably best to require multi-classing for abilities that do increase these odds.
The mistake d20 makes is the same mistake munchkins made 30 years ago. Munchkinism was the confusion of high level PCs and equipment with high level play (not gaining equipment above one's level, which is just good play). By abstracting skills and then tying automatic increases into class levels they stopped requiring better play for higher levels. All levels have become equally difficult. Not to mention all high level characters are comic book Supers far beyond the human range of ability. (i.e. everyone hears like superman, jumps and tumbles like spiderman, etc.)
The typical argument against role-playing in role-playing games basically goes "systems without skills are DM fiat" and "players play the DM, not the game". Which is pretty ridiculous in my opinion when you consider every game is "playing the designer's rules". For example, if my module says a there are rat traps in a room, I the GM know how they function as the designer defined the traps for me. When players interact with those traps they needn't roll at all during the interaction as they probably have a good idea of what a rat trap is too. But just as my idea of a rat trap in the real world isn't the thing in itself, neither are the Players' ideas of the rat traps in the game world the reality of those traps either. That reality is in the GM's head via the defined world. That reality doesn't change just because it's read off a page or picture vs. physically modeled and then related. Removing DM fiat is the entire purpose for rules in an RPG. That the rules are fully encompassed in the definition of a rat trap (actually, that's more likely in the definition of a painted portrait or other static item) doesn't make them any less real than a dice roll in those abstracted skill games.
All of this is not to say that portions of the world may or may not be abstracted in traditional, role-played, non-skill-using RPGs. It's just those abstracted elements are the "non role-playing" portions of the game. Just as you don't say you're eating or breathing whenever you play. Those actions are assumed or abstracted. But typically the moment food or breathable air becomes a threat it is taken into account with greater rule specificity instead of abstraction (like with starvation rules vs. monthly upkeep costs or suffocation vs. combat fatigue).
