You're not choiceless any more then you are in other cases, anyway. If I blast a unit into oblivion with magic before you can move it, then you didn't have any choices either.
This is a very poor analogy for the situation. There's a big difference between focus firing a unit and killing it, and tying it up with high defense units so it can't move/attack. Units die, but having one that you can't control for consecutive turns because it's getting its AP depleted is not fun.
It's a false choice. Sure you have a "choice" to make it so your stuff can counterattack, but doing so is a bad idea against just attacking first. (Similar to a caster sovereign having the "choice" of spending all their essence. That's another false choice. While you can do it, doing so is such a stupid idea that nobody who knows what they're doing will ever do it. It's a totally meaningless pretend choice, one decision is the correct one.)
But this isn't true, you said so yourself:
The only units that will be counterattacking under this kind of system are meat shields brought to get in between the incoming baddies and the important units. The important units will be attacking and then running for cover because they can't defend themselves after doing something.
I mean, you oversimplified it, but isn't the point of tactical combat to actually be tactical, and not "everyone does everything"? You'd have your heavily armored units mainly trying to protect your ranged damage dealers - they'd spend all their AP attacking while the their protectors would counter-attack.
You also talk as if attacking and counter-attacking is a 1:1 relationship, but this isn't true either. Under the current proposal we're all running off of, counter-attacking takes half as much AP as attacking. So, you would absolutely have a choice between attacking or defending and the benefits of each will be highly situational.
Let's play with a few numbers:
Say you have a unit with 3 AP and 1 combat speed against units with 1 AP and 1 combat speed, for simplicity. That's 3 attacks, or 6 counter-attacks. If the unit is engaging 2 of the other units, you have a choice between: 1) attack 3 times. 2) attack 2 times, have enough AP for 2 counter-attacks, 4) attack once, save 4 counter-attacks, 5) save all AP for counter-attacks. The obvious choice is 2). You get 4 hits in, and since the opponent can only attack once you also counter each of their attacks. Everything else results in a lower total damage output from you.
Now say you have the same unit and against the same 1/1 units, but now there are 6 of them. You have the same choices, but now the obvious best choice is 5), you save all AP so you counter-attack 6 times and maximize your damage that way.
This is far, far, far superior to any "ha-ha, I can lock down your unit and there's nothing you can do about it" mechanic.