In the Burning Wheel family of games, there are various principles that govern "say 'yes'". Burning Wheel uses the DitV approach - say "yes" if nothing is at stake (where stakes are defined by reference to PCs' beliefs, instincts, traits, relationships, etc). Torchbearer uses the "Good Idea" approach - if the players come up with a good idea, the GM unfolds the situation from there to frame the next obstacle. I don't know how Mouse Guard does it, but I'm pretty sure it will have a discussion of it somewhere.
But in this family of games it's also the case that your PC needs to make tests - both successful and unsuccessful - in order to advance. The aesthetic, as Manbearcat has said, is of bold moves against the odds (which contrasts with "good ideas" that mitigate risk). The system significance is that only failed checks give the GM the opportunity to introduce new content that changes and complicates the situation: on successful checks, or if the GM says "yes", then the players get what they wanted. The random, but over time steady, alternation of success, failure => success with a condition, failure => twist, is what drives the game. And this relies on tests being made.
The need to make tests - including tests that are hard - also means that players have to make decisions all the time about spending fate and persona, about getting help to boost their dice pools, etc. This stuff is not just about "in case of disaster, smash glass" but becomes a core part of player decision-making. None of this rules out creative solutions, but creative solutions aren't confined to "good ideas" - they include things like Now's the time to test Circles to try and get a NPC on the scene to help us or Maybe if we frame our approach this way rather than that way we can test Nature, where we're strong, rather than Pathfinder, where we're weak.
This is all very different from Moldvay Basic, and the broadly similar approach you describe of avoiding dice rolls by finding creative solutions. If it's not what you're looking for, then of course these games won't be for you!