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Why draw?

That's where an arbiter is needed though - I don't know if a computer could be programmed to recognise such situations....? Maybe? I think it would require something like a tablebase, where the worst moves on it are selected... and tablebases of the size needed for this sort of position would be impractical (though possible to make). Just hypothesising.
Indeed. There's a reason that established online servers typically intentionally deviate from FIDE rules here, and that reason is the computational cost of determining whether any sequence of legal moves could end in mate.

ICC, for example, does not obey that FIDE rule, and explicitly points out in their documentation both that certain material configurations will result in the ruling of a draw, and that these rules are similar to, but not the same as, FIDE, USCF, and other rule sets.

These games aren't even remotely attempting to be FIDE rated, so there's no reason to adopt all FIDE rules (or to think that FIDE rules are somehow superior).

For example, (I'm being facetious, but I'm sure there are people who would be happy with the following ideas) why not implement a "click-move" rule, where once you've clicked a piece you have to move it? :)

Better yet, premoves aren't allowed in FIDE chess, so why not ban those too? :)

This is one of those cases where I think adhering to FIDE rules is neither feasible nor desirable.

As always, just my $0.02, though.

Cheers!
To be fair, this is a win for white in the position, as long as it is a blitz game. I hope you just trust my expertise as a skilled player and won't question it, but it is possible to win it (e.g. black king h8 with pawn/bishop, white king f8,Bg7). So it is a win, if black wouldn't play Rxa3 over the board as the last movement when his time runs out.

In Rapid or classical chess this is a draw, since playing on time is not accepted. Therefore (as long as you don't forget to claim the draw) the oponnent has 2 choices. Either he accepts, or, if he thinks that you are actually as dumb as getting mated in this position, you will be granted 2 last additional minutes for free and you "defend" yourself from his threats. Since any reasonable human will fear getting mated, the result we be a draw.
Interestingly, it would be a draw under USCF rules.

14E2. King and bishop or king and knight. Opponent has only king and bishop or king and knight, and does not have a forced win. (then the game is drawn)
White to move and draw. FEN: K1k5/8/P7/1n6/8/8/8/8 w - - 0 1

On lichess white just has to run out of time and it's a draw.

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