Except that we know that it doesn't. Initiative occurs when you're drinking in a bar, strolling down a park path, and every other situation where you wouldn't normally expect combat to erupt.
Hence, "in a generalized, abstracted way".
Nothing's going to be a perfect model, but I personally find assuming that initiative more or less represents that to be a lot less odious than what I can see the readied actions bit doing to the game, and trying to finagle that.
Seriously, though, if the rogue is using stealth, they still get to sneak attack with their first attack. And, once combat starts they need flank and flat-footedness is irrelevant.
We actually do have a rogue in a couple of our games, and the initial flat-footedeness of the enemies has been largely irrelevant.
Well they'd at the very least need some way to get concealment for that to work, which is iffy. It's been a really significant source of the rogue's damage in our game, so I really don't like the idea of just taking it away for the asking.
Ah I see. Okay, but so? Even if your rule is that initiative only occurs with actual attacks, I can still have the wizard unarmed slap the fighter every round as we walk along and force initiative all day anyway, and get this same advantage.
That wouldn't be "my rule" either. My rule would be, to quote the combat section "At the start of a battle, each combatant makes an initiative check."
So as a GM, I would look at the Wizard slapping the fighter with no intent to kill, think long and hard about whether, in my judgement, it constituted a "battle", then respond "of course not, that's ridiculous", and if any player tried to claim an initiative check for that "battle" I'd roll my eyes and say "no, now stop fooling around and play seriously".