Not quite 100% accurate. In 1E, PCs could only react to foes in front of them. So, no dex bonuses against foes behind them, a shield bonus against 3 foes max, and no attacking a foe from behind him from running away.
And I agree, nothing stopped PCs from just moving past the front ranks if they were not engaged in melee.
So yes, every PC was this sticky in earlier editions. Now, none of them are quite that sticky. Claiming that fighters should be and other PCs should not does not match the 1E or 2E rules either. The combat rules applied to everyone (which is why I argue for less specialized rules like this house rule and more generic everyone can use them rules). Virtually none of 5E matches 1E or 2E rules completely anyway. So, a bit of an apples and oranges comparison.
So yes, an engaged foe was often a bit stickier in 1E/2E, but in some circumstances, he could be less sticky. An unengaged foe, not so much. And this was a trait for all PCs, not just for fighters.