Except that you can't actually get away from the fighter. If you shift, he possibly hits you and you've moved one square. If you move, he almost certainly hits you and you've moved one square.
The fighter does not "almost certainly hit you". Monsters are not always being flanked, fighters do not always have good Wisdom scores, or even always good to-hit rolls, and many monsters have high ACs.
It has nothing to do with "afraid to be hit" and everything to do with "why be hit for no benefit?" Skirmishers and controllers frequently have ways to move themselves or the defender, as do many higher level extraplanar entities. but once a soldier or brute is next to a fighter, the price of trying to get away tends to be too high much of the time.
This interaction does not take place in a vacuum. There are typically multiple monsters in the fight, which means that the fighter will not always pursue a moving target. So even shifting one square can sometimes get a monster into a better position. Monsters can shift and then charge, or even move and then charge, and their basic attack is often their only attack, so there is very little cost there. Even in the worst case scenario, where the monster has to spend its whole turn getting away from the fighter, all it is giving up is an AO/CC attack from the fighter and a chance to hit the fighter.
Defenders, even if they have multiple enemies marked, can typically only use their defender features (combat challenge/aegis/paladin thing) once per round, so multiple enemies can sometimes time their turns so that the only one who suffers is the one best equipped to take it. Fighters can only make one AO per turn, and monsters have multiple move actions (or even one move and one charge action) so a monster can always get away if it doesn't mind the chance of getting hit.
When I DM, tactically I find that the combats are more dramatic and more interesting if the monsters behave in risky and unexpected ways. In other words, when the monsters behave in risk-averse ways, they get locked down by the "sticky" defenders, everyone else fulfills their role in combat, things become static, and victory becomes a
fait accompli. When the monsters act risky, desperate and aggressive (as I feel they should, or why are they even in this fight?) then it's easy to see how a less optimal dynamic can develop. The slow defender will have to be chasing monsters around, and can often only tie up one at a time. The strikers will be getting hit more, and using more of their movement-related powers. The leaders will be in melee more and using their healing on the non-defenders, where it is less effective. The controllers may be running for their lives, or at the very least, burning resources on defense.
In other words, in my experience, when monsters behave in a riskier fashion, including drawing more attacks from the defenders, they can force the players to burn through more resources. They are effectively more dangerous. As a DM, that is what I want. Thus, fighters in my campaigns frequently get AOs and get to use their combat challenge.