How is the merit of the player's input judged in such a system? A bonus, a DC adjustment?
It would depend greatly on the rules system. For these sorts of theoretical discussions it's worth using Celebrim's Simpliest RPG Rules Ever Devised (SRRED). The rules set consists of only one rule.
Rule #1: For any player proposition, flip a coin. If it is heads, the proposition succeeds. Otherwise, the proposition fails.
It's a complete universal rules system. It is for a lot of different reasons not a very good one I admit, but it does work as a very good means of stopping people from thinking in the box.
So, how is the merit of a player's input judged in this system? It isn't. Regardless of whether you propose to jump a puddle or the Atlantic ocean, you have an equal chance of success.
So, suppose after an enjoyable session playing SRRED, the players get tired of the zaniness and decide that SRRED would be a little more fun if it had just a few more rules. Which of the following rules sound good to you?
Proposed Rule 0: One player is appointed a Referee for the duration of the game.
Proposed Rule #1: For any player proposition, if in the opinion of the Referee the proposition is well within the abilities of the player's character, the proposition always succeeds and no coin flip is necessary.
Proposed Rule #2: For any player proposition, if in the opinion of the Referee the proposition is well outside the abilities of the player's character, the proposition always fails and no coin flip is necessary.
Proposed Rule #3: For any player proposition, if in the opinion of the Referee the proposition has extraordinary merit, the player flip two coins and choose which of the two coins to use after the results of the flip are known.
At this point, we are probably beginning to look more like an RPG. Most RPGs have some variation of the above 4 rules, and in particular the proposed rules 0, 1, and 2 tend to be system invariant and in some cases are just assumed without comment. The fact that they are assumed without comment doesn't make them any less part of the rules of the game.
Either way the player is interacting with a rules element and picking a move from a pre-defined list.
What???
Considering SSRED again, we haven't yet done ANYTHING to define what a valid proposition is. In fact, that's likely to become the first table argument if we were foolish enough to try to play SSRED as written.
You are making statements on the basis of unreflected upon biases about what the system is like and how it is run. We haven't gotten that far.
What I would like to point out here is that Proposed Rule #1 etc. unavoidably create a meta rule beyond the new proposed rule #0 that institutes a Referee.
That meta-rule is simply that the Referees rulings in Proposed Rule #1 etc. become part of the common rules as soon as they are made. In effect, they are rules that act as rules generators, authorizing the Referee to create new rules as he sees fit. But once those rules are made, the players will have a reasonable expectation that the Referee won't alter those rulings on a whim. If the Referee rules that jumping puddles that are 4' across is well within the abilities of Wonderboy, the player of Wonderboy will be unpleasantly surprised if the next time he tries to jump a puddle of the same size he falls in and drowns. The Referees ruling, "Puddles that are 4' across are within the abilities of Wonderboy to jump.", becomes a new rule that we could write down and give a number as soon as it was made.
And this points to one of the problems with rules that act as rules generators.
The number and components of such rules can vary widely.
Sure. Some rules sets are good and some are less good. Some rules sets make different trade offs based on what they consider important. But I'm talking about things that are universal to all RPG rules sets. There is no, "Oh, you have that problem but I don't", here whatever you are insinuating. These problems are unavoidable.