Hey vfabien, thanks for posting!
Yeah - a lot of the game's strategy is about properly reacting to what your opponent just did (and about predicting how they'll be able to react to what you're about to do). Double-turns is an interesting idea, but what Kenbutsu says is true - it's just not really compatible with the Antihero ruleset.
The "Live Games" feature is Antihero's answer to "let's make this move along faster!" ideas. Currently, because we have a small player base, Live Games are lobby-based. But when the game hits 1.0 and every man, woman, child, dog, and parakeet on earth buys a copy, we'll turn automatching on for Live Games as well. (Even if there are some parakeets that don't end up getting the game.)