This is a followup to: How long does the AC increase from the Battle Master fighter's Evasive Footwork maneuver last?
What is the point of the Battle Master fighter's Evasive Footwork maneuver?
If it only lasts till the end of your turn then why use it? Unless it's to avoid opportunity attacks, but trip attack disarming strike, and push attack can all do that as well, and they do something else to. So why bother with additional ac that doesn't last long enough to help you avoid being hit?
Best Answer
Evasive Footwork protects against all opportunity attacks
The alternatives you list only protect against opportunity attacks from a single creature. In contrast, you could use Evasive Footwork to run past a whole group of enemies, and all of their opportunity attacks will be against your increased AC.
Evasive Footwork doesn't require a roll to succeed
A shove attack to knock a creature prone requires a contested ability check. Both of the Battle Master maneuvers you mention require you to first hit with an attack and then have the target fail a saving throw before they will do anything to prevent an opportunity attack. In contrast, Evasive Footwork just works, with no need to succeed on a d20 roll first.
Evasive Footwork does not use your action
All your other suggestions require the use of your action (or part of it) to attack the target you wish to escape from. Usually this isn't a problem, since as a fighter you generally want to spend your action hitting something. But attacking might be undesirable if you want to use your action to do something else, like slotting the Macguffin of Power into the Power Macguffin Receptacle after dodging and weaving your way past the horde guarding it, with AC your enhanced by your Evasive Footwork.
(Credit to @V2Blast for pointing this out.)
You might want to provoke a bunch opportunity attacks (and have them miss)
If you use Evasive Footwork and then run past a bunch of enemies, chances are they will all take a swing at you with their reactions, and most of them will miss against your increased AC. This expends all the enemies' reactions, allowing your squishy allies to move around more freely without provoking opportunity attacks. This could be especially useful if your party needs to make a hasty retreat, since it allows your allies to use their action to dash away rather than take the disengage action.
This use is, of course, very DM-dependent. Realistically, only the most disciplined and well-trained enemies would recognize your distractionary tactic and forgo the opportunity attack, but the DM might (intentionally or not) play less intelligent enemies as if they automatically know you've used an ability to make yourself harder to hit and have them refrain from taking opportunity attacks against you, despite the fact that there is not necessarily an obvious visual tell when using this maneuver.
(Credit to @DanielZastoupil for this idea.)