Can this be a good chess problem?

I am new to the forum (to the game as well), so if something's wrong, please let me know.

The game below has several rookie mistakes from both sides at the beginning, but the ending is very strong - I think. Last 5 moves can be a good, challenging chess problem.

I vaguely remember seeing some chess problems based on lichess user games like this. Do you think it deserves the effort? If so, how can I report it?

Also, please feel free to and comments.

Thank y'all.

Black plays and force check-mates in 6 moves (at most):

Problem should start after White's mistake (17. Kg1)

Ooh that's pretty.

Without using the computer: perhaps 18. Qg3 was a try?

White's Qg3 won't save. Knight f4 mates in 2.

That's the beautiful part of the problem. There is no saving move against black's Qg4!

This is indeed neat, the only "issue" with that for beeing a chess problem is that Qg4 is not "forced". Of course Qg4 is the best way to win this, but in a well posed problem Qg4 has to be the only move keeping the advantage (meaning that everything else throws at least most of that advantage aswell).
In your position 0-0 is still a clear win for black, but if you take away the Rh8 for example, or modify it by giving both rooks away (Kg8,Be7, no rooks), then it is a fine problem. Of course then Qb5+ is replaced by Qb8+ but the rest stays the same

Imho, it perfectly fits for a problem.
#5 you mention other moves that keep the advantage... indeed but a win in 6 moves is better than whatever evaluation.
Also for existing problems on lichess a forced mate in 5 is not the solution if there is a forced mate in 3...
I don't know how the problems are selected and I think I only saw problems from actual parties played on lichess, not from studies.

This was from an actual game. There is no defense against 17. ..Qg4. Longest check mate takes 6 moves, depending on white's choices it may come earlier, but not later. Queen sacrifice is the bonus.

Of course, this can be re-designed to make Qg4 as the only saving move, but then reality is better with complexities.

I stongly disagree with you about the "only move thing".
The reason for such problems is to train your skills. And the reasoning behind chess is- if you find a clearcut way to win (clearcut, that is 100% win), why bother to look for a faster or prettier? In fact, the easiest win is the best one. True, Qg4 is the FASTEST win in the position, but if I have the possibility to win without thinking, you cannot blame me for playing "just" 0-0, or even say this is wrong. There is no reason not to play 0-0.
Another example of the strongest players recently
chess24.com/de/watch/live-tournaments/tata-steel-masters-2017/10/1/7
The last moves so went for only a +2 position (Knight vs pawns), instead of calculating a stonger continuation which would result in (Rook vs Pawns). It doesn't matter how you win as long as you win. And the best way is the way without risks (like miscalculating).
So therefore, the only reason to play Qg4 in your position is only because the tasks says so. Whereas in a modified version (like all chess problems are!), you are beeing forced to find a cunning way out of your position, this is a real game situation (either you win or lose on material), this trains your thinking. In your case, it more deminishes it because you punish rational chess behaviour like every grandmaster has (e.g. Wesley So mentioned above)

@IM TLTGAM

Lichess tactic trainer allows problems with multiple lines, and lets you freely try again if you play a winning move that is not the best move (except for too long checkmates, but that's more of a technical issue), so I don't really get what's the big deal with ambiguous problem. Actually, I like this tactic trainer much more than the one of chess.com precisely because it allows tactics with ambiguous solution like would arise from real game (because they arose from real game!). They go long the philosophy (taught by some grandmasters) "see a good move, look for a better one".

The point of a tactic trainer is to train calculation, not to win. The point of solving problems is not to win a given position, but to increase your chances at winning any position, by analysing a given position, enchancing vison and analytical mind, etc.. For some people, beauty only might even be the point, and many problems explicitely say mate in X, so the task may as well say so.

As for the OP, Lichess tactic trainer used to extract automatically tactics from games, and has now stopped as Thibault consiers the data base is now big enough. But there might be a way to turn it into a puzzle using the study editor and share it on the forum.

fr.lichess.org/qa/28/how-can-i-create-a-puzzle

fr.lichess.org/blog/U4sjakQAAEAAhH9d/how-training-puzzles-are-generated

#9 I do accept your argumentation, but if you don't agree with me, at least the worlds best trainer Mark Dvoretski (died last year), in every of his book for calculation (like also the award winning series "chess evolution" by his pupil Artur Jussupow) you never see such "bullshit" if you allow me to say. If there is a calculation tast, then it is for calculating ahead. If it is tactics, then you need to spot the right ressource in the position. And if you really are into actuall chess problems, they are rarely from actual games. like this one http://www.genialschach.de/probleme.htm . The way you present it sounds like, yes you solved the problem, but I would like you to solve it the way I want it to, which is indeed a BS in every kind of way
And as for "see a good move, look for a better one"- would you say Wesley So played a mistake but settling only on 1 knight in the pawn endgame? Because he just won and currently as the number 2 of the world you cannot say he should improve.