strive to win fast, or lose slowly if you cannot winand why should your opponent do the same from her point of view and counter your very efforts? I am still looking for simple and sound grounds to motivate such a general principle.
We may try to look higher at meta-strategies. Consider the meta-game of playing a series of ten consecutive games with the rule that you win the series iff you win more than half of the games in it.
Now, if it were true that you should always strive to win fast or else lose slowly, whatever the game, then you should as well make the same effort for the meta-game under consideration, which is a game too.
If you happen to be losing one of the games in the series and you are sure to win the whole meta-game because there is no doubt on your superior strength or because you've already won six games in the series, then you should lose that specific single lost game as soon as possible so as to win the final meta-game as fast as possible. Shorten any local battle to shorten the final victory.
Or if you happen to be winning one of the games in the series and you are sure to lose the whole meta-game because there is no doubt on you inferior strength or because you've already lost six games in the series, then you should win that specific single won game as late as possible so as to lose the final meta-game as slowly as possible. Lengthen any local battle to lengthen the final defeat.
These local efforts would contradict the general principle I am trying to justify.
Hence, meta-strategies justify radically different local strategies, and nobody can consistently follow the general principle I started the post with! Unless in unrealistic isolation from sub-games and meta-games.