David Richerby wrote:

If the position on the board was the same but the players both had
only one minute left (so there's no question of one player having
managed his time better than the other), do you believe that the game
should be won on time by the player who's able to wiggle his king
faster? If so, why does the same not apply to cases where no
checkmate is even theoretically possible (e.g., two bare kings)? If
not, doesn't this demonstrate that the clock is actually less a part
of the game than is trying to checkmate the opponent's king?

It seems to me that, without a rule such as the USCF insufficient
winning chances rule or the similar FIDE article 10.2, good time
management is impossible in any game with a time control of `... and
then X minutes for the rest of the game.' In such a game, you could
never know how many moves your opponent will insist on playing in a
dead-drawn endgame so you'd never be able to leave enough time for
that. OK, so the fifty-move and repetition rules help but, even in a
simple ending, a player could drag things out for maybe a hundred
moves before either became available.

While I totally agree with you concerning the need for FIDE article
10.2, I don't think that the example in the first paragraph shows
that "the clock is actually less a part of the game than is trying
to checkmate the opponent's king." Your example is one where
trying to checkmate the opponent's king is no longer a viable
option.

With a modern chess clock that adds time on each move, you
cannot lose on time in a position that allows you to mindlessly
move your king around. In that case FIDE article 10.2 just
makes the inevitable draw happen sooner.