Do those sheets tell a PC what he can and can't do? How often do the GMs go, "let's just make a roll and see what happens," versus "what does your character sheet say you can do?"
Sometimes in broad, yes. There may be a lot of potential cases where trying to do things outside your training may land in default abilities (whether its in skill minimums or attribute rolls), so to some extent there's never a case where the sheet isn't addressing your need in one way or another. There may be cases where questions of application aren't clear (which I feel is usually a consequence of the definition of what lands in a given skill is muddy) or where a situation is so far outside of the normal play of the game that interpolation is required, but in the properly designed one, there's never a need for raw game-design-on-the-fly is needed simply to resolve something.
Basically, the sheet will rarely (I say rarely because in some cases where non-cinematic assumptions are in play, there may be cases where the lack of a particular skill translates into an autofail, because they are things that require a sufficient degree of technical training that there is no degree of reasonable success possible--in things resembling the real world at all closely there is no chance within the resolution range of most games that someone without the skill to pilot helicopters will successfully do so; a more cinematic system may let you take a shot at it anyway (as I recall Savage Worlds will let you roll a D4-2 on that one, which means with its open ended die roll you might be able to pull it off, but don't hold your breath) tell you you can't do something at all, but it may well tell you your chance of success is pretty poor. In the Hero System there are usually some of what are called Everyman Skills that allow anyone raised in the culture that gets them to succeed in them on 8 or less on 3D6; in RuneQuest even though you haven't been trained to Swim you'll have a 10% plus your appropriate attribute modifiers chance (probably for a PC around 20% total) and the rules on Swimming will tell you when you don't need to make a roll.
So the sheet will tell you an awful lot (in conjunction with the rules) about whether something is likely or possible in all but very extreme cases.
I think it's the "forcing" thing that plays into the "oppression" aspect of the thread.
Do we have any Simply6 players in the thread? That game has a tiny character sheet. Are the Judges of the game as forgiving as I imagine, or as the character sheet suggests?
As I noted, a game can have a very loosey-goosey approach to how flexible its traits are as a deliberate design issue, and some cinematic games in particular lean into that pretty heavily, but even with those the sheet is normally telling you some strong things about what you're liable to succeed and fail at; they're just covering broader ground in doing so. But bad skills that cover a lot of ground are still telling you your success chance on those is poor. They may well not have much that outright says you can't do anything at all (but even in such games there will often be some binary abilities involving paranormal actions, say) but that's more a choice of playstyle than saying that games that actually want there to be a few things that are impossible or difficult without investing in the ability to do them are oppressive.