Winning Despite Losing On Time?

In live chess, should a side win if they run out of time, but their opponents last move would force them to checkmate them next move? For example:

If after white blunders Qxh7+ and black flag falls, should he win since he literally has no choice but to checkmate white next move, as Qxh7# is the only legal move? What about multi'move sequences like below:

Every move is forced, so should black win on time if he flags after the first Qxh7+ move by white, since the only possible outcome at that point is for black to win? What do you think?

According to FIDE rules this would be a draw.

Online chess is different.

Given that white pawn grabbed the queen and the rook did the white queen white owns that game.

2nd game

Well one possible reason it shouldn't be a win is because a player could let his time run out because he doesn't understand the position right away, which does speak to chess ability. Players do sometimes think on the only legal moves if it takes them a while to realize it's the only legal move, or use that time to think about future moves. And I just realized that with my logic it would follow that the site program "trigger moves" where the site would automatically make the move if there's only 1 legal move, but this would be confusing and weird, so maybe I'm wrong. The real problem is it would be extremely difficult to program every possible position that results in a forced stalemate/checkmate next move. And it would also be hard to account for all the dead positions. And these positions could be several moves long, so it seems impossible. For example, a multimove forced stalemate:

I say win for black.

i say give you an option (in settings) of playing only legal moves, if they exist and they will take 0.1 secs like premoves (this should be easy given the programming can show all legal moves of a piece when clicked, and only legal moves are shown in game review

That still requires the realization that that is the only legal move. "Trigger moves" would automatically be played each time there is only one legal move in the position. But I already explained why that wouldn't work actually, pieces moving by themselves would be confusing to both players.

Black ran out of time so cannot win in any circumstances.

Your first example would be a draw under FIDE rules and USCF rules, but a win for white on this site.

I think white should win because black ran out of time. At the end of the game it seems like black should win, because they have no other option but to checkmate. But, they ran out of time by taking too long earlier in the game, when they DID have other options.

I think once the flag falls the game is over, it's not possible to checkmate after the game is over.

I honestly don't understand the time management argument. Both players could have literally spent the exact same amount of time on every move and White wins because he moved first. This isn't a personal biased thing, I just brought it up for discussion only. In fact I even realized that yeah it might be stupid to let black win here because he may have also let his time run out naturally if he didn't see the move due to being bad at chess, for example. But definitely, if the opponent has no way to checkmate you, it should be a draw. You've secured a draw if your opponent has a sole king left, so you shouldn't lose if you run out of time. If you have 9 queens and your opponent has a pawn and you run out of time, you should lose, but not if you have a queen and your opponent has a knight.

That's what you're saying, correct?

In the Alireza Firouzja vs Magnus Carlsen blitz game controversy, I fully agree Magnus earned the win with the black pieces:

Because he could theoretically checkmate white like this. As far as things like touching the promoted piece with the same hand as the clock or picking up the pieces before hitting it, I don't know how I feel about all that semi-OCD stuff, but I definitely agree that if checkmate is possible in anyway, even by helping your opponent win, you should lose if you flag.