Which reasons are these?
Well, the moves are all mocapped, so with the amount of time spent in the studio it seems unlikely that they would have a plethora of different strikes and only one takedown for each situation (armed/unarmed front/back). Martial Artists also tend to know a variety of takedowns, and many like to show them off. Add to that that the CQC is it's own skill and level progression is supposed to grant new combos etc., and it seems like too significant a portion of the game to skimp on visually. Ao2 and K&L didn't even have much in the way of mechanics governing CQC, it was just something you used when you ended up too close. In the case of AP it's a "weapon" skill with its own progression like pistols and assault rifles.
That's just my edumacated guesswork though, Sawyer might step in at any moment to tell us (hint hint).
The game currently features multiple takedowns. I even did the mocap for one of them.
Nice. Do we win anything if we can figure out which one when the game releases?
It's the one where Thorton takes a bad guy down by stabbing him with a pocket protector. It's, at the same time, geeky and awesome because it takes the "everything is a weapon" mantra to the next level.