I don't really get this. What, other than presentation, is so different about 4e that makes grid-less combat so impossible?
Isn't it simply a question of precision?
Yes, and precision makes all the difference. In a game where you have a "Damage: 2[W]" power, and a power that says "Damage: 1[W] + push target 2 squares", which one would you pick? In a game that uses no grids, the second power is less useful, because it relies solely on the subjectivity of the DM to decide it's utility, and the ability of the other players to remember to take advantage of it. If there's a grid and minis, the rogue sees this and says, "ooh, now I'm flanking that foe" and uses his sneak attack. With no grid, the DM:
1) has to remind the rogue he's in flank position
2) has to remember who else is now close to the pushed foe, enemies and foes alike
3) what effects this has on the combat.
If the DM flubs this, the players aren't going to know it, and when they later find out "ooh, I'm sorry guys, I should have let you know that put him really close to the chasm, and someone could've knocked him in" or "oops, Daren's rogue should have been able to sneak attack him" then it's a pain to adjudicate. In the end, every power with a move attached, or dependent on positioning like a charge, is liable to be dropped in that game in favor of powers that just do straight damage or status effects.
Now, if there were only a few move-related powers, it's no big deal, but 4E has DOZENS of pushes, pulls, shifts, charges in powers for EACH character class, to the point where it can be laborious to properly judge the worth of any given power if the only "grid" is in the DM's mind.