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Should be a draw.

In defense of the current rules, I like to fantasize this way:

When one side runs out of the time in which their army is under their control, that means their army will make random moves henceforth.

A random-mover is generally very easy to beat, unless, of course, there is no mating sequence.
#15 if you have a pawn, there's a sequence of moves where you give mate. It doesn't matter what else is in the position, because it's assumed the flagged player will cooperate. So in the position with two queens, White will ignore the pawn and let it promote and deliver checkmate.

If the condition was you need a forced mate, that would probably be fairly simple with modern engines on the server and tablebases. I'd prefer that, but the present system's better than fudging it with "unforced mate unless the flagged player has two extra queens", or something like that - it's too arbitrary, when currently people know to capture all the pawns if they're down on time.
Anyway back to the point, there ARE situations an arbiter will rule as a draw. But online there is no attempt to rule anything as a draw.
Claiming is often futile

-in blitz & rapid nonexistent
-playing with increment nonexistent
-lots of tournaments exclude it in advance
-only when below 2 mins left a claim is allowed
-an arbiter can decide to play on

I asked different arbiters how they would decide in a case of pawnless BB-B with few seconds left for the guy with 1 Bishop.

Some would decide on draw instantly, some would decide to play on a couple of moves which means he is lost.

PS: N vs a/h pawn is the textbook example for NOT to decide on an early draw. Is is even contained in endgame books. See my game above?

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