Reynard said:
Leaving it -- and all skill things like it -- out entirely, dealing with it in a reasonable way between player and DM, makes the game more fun and improves the quality and value of play.
I would say that the problem isn't with the existence of the skills, but rather with that specific implementation of them. The 2e NWP skills were, quite frankly, piss. Far, far too narrow and nowhere near enough choices.
However, I think you're throwing the baby out with the bathwater. Why not have an "Outdoor Adventurers" stat? This mechanic gives you your relative skill at doing anything outdoorsey that is within reason. Depending on the level of the stat vs the difficulty of the job, you get a mechanic to distinguish my character from yours. Maybe my fighter is a knight who always had a squire. What do I know about cooking rabbits? I had servants for that.
OTOH, your woodsey Robin Hood type has a really high score and can knock up a two storey back split in the middle of the woods using spit and toothpicks.
If there are no mechanics at all, then IME, players simply won't try to do anything.
Take the example of searching the room. The first time, the party goes through the room description, point by point, and searches everything. The second time, they do the same thing. The third time, they turn to the DM and say, "We search the room the same way we did the last two rooms." And suddenly that "Player Skill" thing goes away. It's subsumed by standard proceedures.
Any potential gain in creativity will quickly be buried by repetition. Particularly in a dungeon crawl where you generally have dozens of rooms, most of which aren't really all that different - four walls, ceiling, basic furnishings, maybe a closet.
I really don't think you gain anything by using systemless resolution. At best, you gain something once or twice and then it goes away.