Skill systems aren't a mechanism for the referee to let player-characters do stuff. Player characters were always doing stuff. Skills are a way to prevent player characters from doing stuff. by discriminating among them in different ways.
Hmmm. I'm not sure I agree with this. Skills are merely those abilities characters are assumed to have used often enough to have a level of proficiency using, but it doesn't mean they're restricted or prevented from using skills they have no proficiency in. Of course, in the official 2e system, a character can't just bolt on any old skill they desire; unfortunately, they have restricted access by level. I think it best to allow characters to try anything they wish within common sense and reason. Characters that say they would like to try and learn lumberjacking without an axe or saw, well, good luck hacking at that 120' alder with your shortsword. You will be there awhile, and you won't gain a single point in it.
As for the original question, yes I play and run 2e with house rules. It's the system I've always preferred.