Why I find 3e combat too static
1. Movement is penalized. This is perhaps the biggest one, but, moving, particularly at higher levels, is almost always a poor choice. You lose your iterative attacks if you move. It is very rare that moving more than a 5 foot step is worth losing half or two thirds of your potential damage.
This happens some times. But I'd say that claiming this fits my experience as a rule would be hugely mistaken.
The massive flaw in this claim is that it presumes all targets are equal in merit so attacking the guy right in front of you is equally valid as attacking the guy over there. Even from a purely gamist pov that is frequently far from true. The guy over there may be a much more important threat and need to be dealt with *right now*.
But if you put story in the game then the need for movement becomes the far more common situation. The need to go after a specific target, protect something, acquire something, interrupt something, etc... makes motion a nearly constant obligation.
You and I have recently had some "AHA!" moments regarding the radical differences in what we want from our game experience. I think this comes back down to that. If I were to play 3E with a mindset that combat happened in a vacuum and the goal was simply to kill everything in the way and then high five all around, then this would probably be a much bigger issue in my games.
2. Monsters are doubly penalized by movement. Monsters don't have iterative attacks, but, even low level monsters as early as CR1 have multiple attacks. The standard claw/claw/bite routine for most monsters. And, because of the way monsters are made, their extra attacks are not as penalized as a PC's iterative attacks, meaning that their multiple attacks are more likely to hit. It's a fairly rare monster that gets one big whammy (although not unheard of). Most get multiple little whammys that add up in a hurry. But, if the creature moves, it drops its damage output massively - going from 3 chances to hit down to 1.
This is actually just point #1 repeated and the same responses apply.
3. There are rarely any advantages to moving. Beyond shifting to flank, why would a character move? He's already engaged the enemy, so, presumably, it's better to kill this one first than try to move on to something else. And, "protect the caster" doesn't really work. There's nothing the fighter can do to stop the baddy from just walking around him, if the DM wants to munch down on caster stew.
I think this is already been addressed. But it is amusing to note that in claiming how ineffective moving is your example requires accepting how easy and valuable the "baddy" finds moving.
4. Most 3e encounters feature very small numbers of opponents. I base this on multiple modules including nearly a hundred Dungeon adventures. The overwhelming majority (about 80 % IIRC) of encounters feature 1-3 opponents. Moving around doesn't make a whole lot of sense if you only have one opponent - where are you moving to?
There is a lot wrong with this example.
First, set pieces against a single foe are classic iconic elements of the game. So that will skew the numbers for reasons that have nothing whatsoever to do with mechanics. I can't speak for 4E adventures, but I'd certainly HOPE they kept that classic element as a common theme.
But also, even if you were completely right, the choices that WotC and/or Paizo make in adventure design do not limit the capacity of the system.
And even then the presumption that you just stand there and smash the monster is going to be true some of the time, but calling it a truth goes back to smacking of the pure gamism "kill the monster, high 5" that may work for you but has no representative value for me.
Also, while 1 foe should get a pass for story reasons, as soon as you got to 2 your point about not moving starts to drop off fast. Even including three as a reason not to move requires a charitable view.
But, you are not right anyway.
I went and randomly grabbed three sequential Dungeon issues from my of 3E days stack. I hit on 148-150.
Total encounters = 92 (I counted random encounter tables as 1 encounter with the avg # of foes).
Number of single foe fights 34.
Avg # of foes 3.8
Maximum # 26. (an outlier no doubt, several were 10 -14)
Portion with less than 4 foes: 55%. (Not exactly "overwhelming", just barely even majority)
Portion of non-set piece single monster fights that also had less then 4 (i.e. 2 or 3 foes) 29%.
If you had been right, it wouldn't matter.
But you were also wrong.
5. It is almost always better to gang up on a single target than damage multiple targets. There are exceptions to this, but, focus fire is almost always the best tactic to use. Half killing two ogres is far less effective than killing one and leaving one fresh. So, again, why move? You get into contact with one baddy and you stick with him until he's no longer breathing. Shifting targets by moving is most often a poor tactical choice.
This may be valid. But it says nothing whatsoever about game mechanics and speaks simply to Military school 101 level tactics. I'd presume this is just as true for 4E. And for any game that this isn't true, I'd see that as a strike against the merits of that game.
Edit: this also contradicts your item #1 which claims you should just attack whoever is in your face.
So, there it is. There are my 5 reasons why I think 3e combat tends to be static. Can you get around these issues? Quite possibly. If you use a lot of humanoids (no worries about losing multiple attacks until fairly high level), and large numbers of them at a time, you can likely get a more mobile encounter. Not my personal preferred solution since I like monsters too much.

But, it should go a long way.
It may describe your game.
But beyond that... shrug