I've used minis and grids throughout my D&D "career". I've still got some of my original minis (25 years old, now). I used to create my own battle grids on white posterboard.
I also used minis and grids for other games (Shadowrun, Marvel Super Heroes, Nightlife, etc.). To me, it just makes sense. Every game I have ever played in without using minis has been a confusing mess in battles.
I even use minis for non-combat situations. When the party is trying to diplomacize their way through the town gate, I like them to see the number of guards standing around. It also reminds everyone who is actually in the store getting info from the merchant -- if their mini is not on the grid during the discussion, they remember better that their character is off elsewhere -- helps keep extra voices quiet. Setting up the scene with minis and a basic sketch takes about 5-20 seconds depending on how many persons are in the scene.
As for those who say, "The imagination is better than any grid or minis." or some such...
How is it you can imagine so easily that the bearded and balding, 200 pound guy next to you is a handsome, thin, elf wizard, but somehow looking at a mini of a handsome, thin, elf wizard hinders your imagination?
I have never, ever found a game without minis to be more imaginative or evocative than a game with minis. I have never, ever had a DM without minis be able to completely accurately describe a scene and battle well enough that everyone at the table understood and imagined the situation "correctly" or the same way.
Quasqueton