Again, this isn't simply an abstraction. You can't divorce this stupid rule from in-game reality. Where you call a distance "one square" or "five feet" doesn't matter ... what matters is that if "one square" isn't always approximately the same as "one square," time-space goes Cthulhu.
Consider: You're Fred Fighter, adventuring in a dungeon with Roger Rogue. There's a corridor that forks, so you explore. The DM tells you that both rooms are 5 squares by 5 squares, but one is diagonal to the other. (The DM is looking at his cool WotC 4E adventure, with blown-up encounter maps, pre-placed monsters and traps, and so on. Or he's looking at his own pre-drawn map. Whichever.)
Roger isn't too confident in his trapfinding skills, so he asks Fred to tie a 25-foot piece of rope to his belt and hold on from outside as Roger searches the rooms. Just to start, Roger walks to the far wall of each room. 5 squares, right?
Does the rope reach that far in the orthogonal room?
Does the rope reach that far in the diagonal room?
If the answer to both is "yes,"
Then both rooms must be 25 feet square, right?
So "one square" must have an actual, in-game, "real" distance meaning, right?
Yet the room built along the diagonal is twice as large as the other room. Roger knows it's twice as large, because if he wants to search square-by-square, he has to search twice as many (thus twice as long) in the diagonal room.
If the answer to one of those questions is "no,"
Then it's absolutely, observably true -- from the characters' perspective -- that they're able to move faster when moving in certain direction. (Presumably diagonally.)
Those are "yes or no" questions, and both answers have bizarre, space-time warping repercussions that are actually observable to the people that inhabit the universe in question. That's just ... too much.
It's not the simple, fudgeable abstraction of a diagonal 5-foot step, or one free diagonal "realignment" along the grid during movement, or cheating a tiny bit for creatures with 10-foot reach. It's not the absolutely necessary abstraction of discrete spaces for creatures to occupy or of cyclical, turn-based actions.
The 1-1-1-1 rule is deliberately and unnecessarily introducing huge errors into what had been a simple and reasonably accurate simulation ... errors so huge that no person in the game universe with an average intellect can possibly fail to notice them. Dwarves really
will build their fortresses aligned to The Great World Grid, or some such, in order to get maximum ability to defend. Adventurers really will work out and use tactics that differ depending on whether an encounter is closing on diagonals or not.
If that doesn't bother people -- or at least seriously amuse people; for me it's both -- there's just not much more to say.
(It's worth pointing out, though, that in two recent and active polls:
(1) 4E adopters outnumber 4E rejectors by 4-to-1, yet
(2) People prefer 1-2-1-2 movement by more than 2-to-1. (And that's not counting people who would rather use hexes than use squares at all, at least some of whom have come around to that because of 1-1-1-1 movement.
So it's not 4E-haters that are rejecting this rule. (I wasn't a 4E-hater
until this rule.))