Addressing a couple points.
If you set the puzzles to stop after each one, there's an Analysis option on them.
Regarding themes, puzzles are already very artificial, with you knowing there's something in the position to find. Adding additional hints makes it much easier to solve them.
Chess puzzles are fun, but Chess.com’s implementation of puzzles can make me want to pull my hair out. The only feedback ever given is “(move) is incorrect.” There is never any feedback given about why a move is incorrect. Sometimes I’ll see the solution and still not understand what the point of the puzzle is to begin with.
Here are some ways that this experience could be improved across 500,000+ puzzles:
• Have the engine on max difficulty make the continuation after a wrong move. Does a move hang a valuable piece? Take the piece. Is a solution not really checkmate? Thwart the mate attempt. Showing the player exactly why their move is wrong would make puzzles much more instructive.
• State the purpose of the puzzle. Puzzles on Chess.com are already categorized. This category can be used to provide basic information about what the puzzle is trying to teach, like, “You’re winning in this position. Find checkmate!” or, “You’re losing very badly in this position! Find stalemate!” or, “The opponent blundered valuable material in this position. Find a way to take it!” This is especially important for more abstract concepts like deflection or Zugzwang/Zwischenzug, which beginning players might not understand even if they see the solution to the puzzle play out in front of them.
• Use the engine evaluation in selected circumstances. Generic statements like, “White had the advantage, but now the game is close to equal,” or, “That is not the right idea” are usually not very helpful, but feedback can be made to be very useful in some situations. For example, if the evaluation is M2 but the player makes a wrong move, the feedback can be something like, “You missed a checkmate in two moves,” or, “That move gives checkmate in four moves, but there is a faster way.” Or if the engine evaluation swings wildly in the wrong direction, the game can give feedback like, “Your opponent now has checkmate in three moves,” or, “You just gave your opponent a game-winning advantage” along with the opportunity to see the continuation against the computer.
• Allow playing against the computer or using the analysis board immediately. Presently, I have to exit puzzles, go into my stats, find the puzzle I missed, and then reload it before I can bring it up on the analysis board. Players automatically lose puzzle rating points on an incorrect puzzle move anyway, so why not give them the opportunity to quickly learn from the puzzle to improve? For the same reason, it should be much easier to replay a puzzle and try again.
Chess.com’s existing puzzles are like having Levy Rozman as a chess coach, but all he ever says to is, “Wrong move. Wrong move. Wrong move. Wrong move. Wrong move.” Implementing some fairly simple improvements could make it feel like Levy Rozman is personally teaching you chess. (I mean, it wouldn’t be AS good, but still…) Improvements like this could make a lot more people want to pay for premium membership.