Many people didn't like the move limits...
I do like your idea of being lenient at the beginning, but it also might be a problem with communication
Running out of moves was never meant to be a faliure state, the same way dying is super meat boy does't mean you failed the level, or how dying in outer wilds doesn't mean you failed the game. Runnning out of moves is just a perfectly natural and expected part of the puzzle solving process
But we completely failed to communicate this in the game, instead we have an "out of moves" screen that looks very much like a game over screen, which communicates to the player that they did bad and thet they failed. Maybe we should've done something closer to what Baba Is You does, where it simly stops the music and then reminds you of what button to press to restart the level.