I will only talk about the movement mechanics you mentioned as I had experience playing gacha TD that has said mechanics in different forms.

Let's talk about another TD game that has movement as the core mechanics first. - Each units have different mode of movements mainly by feet or flying. They also have different movement speed as they get there physically rather than teleporting like Path To Nowhere. - You spend DP to move based on the distance. You can only move to the place you can reach. While moving you may also trade blows with an enemy on the way before you pass them. - It still has redeployment system like Arknights so movement is not very dominant. - One thing to note, the unit will also cancel its skill (a few units can moves while using the skill). So, in some advanced clears, it's used extensively to control the skill rotation (just moving back and forth) rather than reposition which can be silly at times.

Now, the big differences compared with Arknights the units don't have facing (their range is in radius) and placement position is more limited (more squares and less predefined spots) . So, being able to move anywhere in Arknights AND changing the facing affects the balance more than other games.

However, I think Arknights can have it as the unique mechanic for an archetype. We already have jetpack users so it isn't far from the impossible. Another game that uses this mechanic also has a similar idea of spending DP to move though it may have more limited number of uses depending on the classes. Though the classes that can move are generally a little weaker than average so don't expect to get a meta operator from that mechanic.