Regarding the first part, I agree. Analyzing all possible checks by me and my opponent is an excellent strategy for solving puzzles too.
Regarding the second part, I do not agree. Please post an example of a lichess CAPTCHA where the correct move is a legal move but that correct move is not a check.
All moves, aside from moves that solve a problem (i.e. check mate) are subjectively correct.
You can make-up your own puzzle. Such as: "Black to move and en passant," or "White to move and fork en guarde." What if you have two passed pawns on the same rank, with white pawns on either side? How do you determine which one is the "correct" move? What if both knights can fork the queen? What if one fork leads to a mate by taking a pawn, but the other fork leads to taking a major piece? See? Subjective.
IMO: We need 2-or-3-move forced check mate CAPTCHA's.
@hangrad @MrCharles Thank you for giving me the answer for this tricky knight CAPTCHA. I would have never been able to comment here without your help!
^^^^ LMAO