It's probably worth noting that having to think about the math of moving (which 1-2-1-2 requires for almost everyone, even if they don't want to admit it) breaks your sense of immersion. Any time in which you have to think about the rules of the game, really. It's the biggest flaw in rules for simulation - it might be accurate to have a bevy of modifiers like so:
Attack Roll:
Base +18
Sweaty Grip -1
Unstable Footing (Cobblestone) -1
Opponent's Gaze is focused 30 degrees off +1
Mild Crossbreeze -1
Fighting Off a Cold -2
Lunch Was Too Spicy -1
Slept at a Holiday Inn Express +2
Etc.
But tracking the modifiers would not only detract from overall gameplay by taking time, but also make it impossible to divorce the mind enough from the game to immerse oneself in it.
I'd advise everyone who finds '1-1-1-1' to break their suspension of disbelief to play with it for two sessions (preferably without actively trying to ruin your enjoyment by focusing on it). Worst case scenario, it will provide you more ammo for these debates and you can say "I've played it, and it bugged me horribly."
I'll admit I didn't give 2-2-2-2 a full chance... only 1 session... but yeah, I really didn't like how it played out. I like hexes fine in play, but not when drawing maps so I could probably live with them for homebrew games and less so for modules unless the modules were hex-based. I've played 1-1-1-1 and 1-2-1-2 both for months (or years), and can play either way. 1-1-1-1 has notable play advantages and after a couple 'What the' moments, it no longer bothers me, not even a little.