Action timer in combat.

Wouldn't it be simpler to just give each player a set amount of time for the battle, like 20 minutes, and whoever runs out of time loses? That way, people wouldn't drag it out.

No. The main benefit is not saving 30 minutes (although that's a plus too), but rather improving the quality of battles. Most people have learned how to move units around, but very few can actually fight effectively (and I'm not one of them, by the way). That's why ATG will always be one of the strongest players in history, because no one has reached that level of micro-management since. And he did it (and still does) very quickly, and that's what makes it so impressive. To come up with a simple solution after 25 minutes (and in the process, lull the opponent into a false sense of security and maximize their frustration) is not impressive at all.