Personally I think it is not the best design to create a problem (multi-action penalty) to solve another problem (static combat). But at this point how do we fix it and why would we fix it?
I'm not entirely sure why static combat is bad. Certain kinds of combat are realistically static. But on the assumption that it is bad and that more movement is desired, I'll play along...
I think the heart of the issue is that character (PC, NPC) actions are not more interleaved. Movement is largely adjustment in position to gain an advantage or alleviate a disadvantage. So, wouldn't it make sense for characters to _do less_ per action so that there was more of an opportunity to adjust your position compared to the number of attacks they face? (I'm spit-balling here. Shoot this full of wholes.)
If you only had two actions, there would be more opportunity to make positional adjustments in relation to the number of attacks being conducted. There would be more opportunities to move out of a disadvantage compared to the number of attacks received and then you might see melee better represent a duel or small action where mobility is more prominent.
My observation of the three-action system has been that Rogues become more mobile in pursuit of a flank without having to resort to immersion-breaking acrobatics because there are few AoO's. But once the rogue is in position, they fall into static patterns like everyone else. None of the other classes appear to be played any different than before with the possible exception of Fighters/Rangers no longer needing to have Spring Attack to quickly close with a very large creature, again because there are few AoO's.
Basically I'm positing that if you want more mobility in your game, you want fewer attacks per action, allowing those on the defense to adjust more frequently, which in-turn will lead to more adjustments by those on the offense.
But recognize that terrain makes for better places to defend. Expect defenders to use terrain and that will also make combat more static. You're going to defend a doorway, for instance to limit the number of attackers that will reach you.
Anyways, that's a theory, half-baked as it may be.
