Why do you think so?
The action point system wouldn't add more as far as I can tell
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What I mean is that the change from the action point system to a 2 action-system made a lot of changes necessary to actually keep the game working.
A very simple example is: Looking around in Jagged Alliance for example costs one action point. 1/20 of a turn. This is not possible in XCom. Solution: You see everything in 360 Degrees. Sneaking in a classical way not possible anymore.
The cover change is a similar story: In Point based systems you might have cover, but you can also run out of cover, shoot, and possibly run back, maybe get interrupted when doing so. But in XCom there is no "few AP left for interrupt" instead you have to a whole action for it. Also not being able to run-shoot-run requires you to have good cover to shoot from. On the other hand, that also means that it must be possible to hit you in this cover. So you can shoot someone even if there is absolutely no LOS between you and your opponent, he will basically put his hands in the air to grab the bullet. Of course you could consider this as "symbolized way of getting interrupted".
Not being able to move tile by tile also changes that you need simplified hit chances, as it's hard to adjust the position by one tile. So XCom has a simplified cover calculation (projectile path plays no role at all) and a simplified tohit calculation (depending on the angle you are either deep in cover or totally flanked).
With an AP system it would be possible to be "reasonable" cautious. Just moving from cover to cover, adjust the position minimaly. Maybe even take points over to the next turn, so that you get the best shot at your opponents.
Do to not having it points but "whole movements" and simplified tohit systems, enemies in the open are trivial to be hit. So this is "fixed" in XCom by giving enemies an extra movement turn when they become active, putting the player into a disadvantage.
And due to this "fix" it would make sense to only move your troops extremyl carefully. Only explore with one, and don't do anything with the others, so that when the enemies are triggered, your other characters still have both actions to adapt to this free move / use overwatch as Zloth said.
This however would break the fix on the one hand, and in addition would also make each combat feel very tiresome.
So the crutch for the enemy-move-crutch which again is a crutch for a lack of AP system, is to just add a turn limit to force the player to move forward each turn.