To keep it simple, I'll only address a little of this.
I want to use minis only when I wish to use them, because an encounter is truly worth lingering over. I don't want to use minis for every encounter, nor do I want to eliminate minor encounters because they take too much time to resolve.
This is where the single biggest logical disconnect is coming in, for me (besides the various revisionist histories, but I'm not about to tackle that Gordian knot).
Minor encounters can, in fact,
be minor encounters in 4e. Resolved quickly and easily, even with minis/tokens/etc. Minions are the most obvious example without any rules tweak at all. If you're willing to tweak slightly, you can get an effect very similar by nerfing defenses or hp values, and maybe removing a power from an NPC if it has something that requires tracking or will lower PC expected damage. But all of that can be done on the fly, too. You don't even need to add prep time.
Incidentally, IME it's not the grid that adds time to 4e combats, it's adjudicating all the temporary effects. Weakened until next turn, slowed (save ends), etc. That's the system "problem" that ate the most time, IME. Mainly because I haven't played with anyone who did a good job of tracking all that, and we had a lot of pauses for "Did you save?" "Save from what?" "That was two turns ago!" etc.
If you want to keep a specific 4e combat fast and simple because it's not a set piece, cut down on or eliminate those effects.
Back to the grid, though... I have bumped into the kind of player who sees a grid and turns into an obsessive about movement, counting and recounting spaces and driving the whole table nuts by taking 4x as long as anyone else to take their turn, but that problem exists with the same people playing Clue, too. That's a player problem, not a grid problem.
Also, I've seen people do 3D combats with a grid. It requires some fudging when it comes to forced movement and such, and it requires some additional imagination to remember, for example, that the apparently flat plane your mini is on represents a slope at a 45 degree angle, or whatever, but I think it's rather extreme to suggest that the grid makes those kinds of combat impossible or even all that hard. Overhangs are a bit of a PITA, but nothing we can't solve right quick with paper, tape, and maybe some properly bent paper clips (I admit, having a table that enjoys -and can rapidly accomplish- some construction is a help here. For the right kind of nerd, though, this is very much a feature and not a bug.)
But again, I think a lot of this comes back to our very different histories with the game. I want to know to a high degree of precision, what is going to happen when I use my abilities as a player. And all the options I have even with a melee character (usually my preference) to affect the battlefield in 4e makes this even more important. I have never seen a DM running combats in his head who could maintain an acceptable level of consistency, and I've never tried, myself, because for me, moving things around on a map of some kind is easier and more fun, allowing me to spend my mental energy elsewhere.
There's definitely a diff'rent strokes element to the situation, but I think overall you are exaggerating the limitations of the grid (or mislabeling other problems as grid problems) and underplaying its strengths. Likewise, I tend to overemphasize the strengths, and I'd guess reality lies somewhere in the middle.