I think in this game Attack Speed is less about doubling (unless you're specifically in the Swordmaster/Assassin/Sniper lines), and more about preventing doubling?
Combat Arts don't allow for follow up attacks. Battalions are about putting in heavy pain without a possible crackback. So being able to double is useful on enemy phase, but in most other cases (again, unless you're a Swordmaster/Assassin/Sniper) you don't really get to employ it?