Some people say that the popularity of the OSR is due to nostalgia. I'm not so sure.
I started playing roleplaying games with AD&D, but eventually got dissatisfied with it and moved on to other RPGs, wanting more options and verisimilitude. I got back into D&D with 3.5E, but eventually got dissatisfied with it because of its complexity and power creep. 1
I've been enjoying Swords & Wizardry White Box and Labyrinth Lord recently, rediscovering the things I did like about AD&D back in the day, but also enjoying the different nature of S&W WB (more like OD&D) and Labyrinth Lord (more like Basic/Expert) from AD&D, and also liking some of the other variants, like Lamentations of the Flame Princess.
But I have absolutely no desire to pull out my AD&D books and play that exact game. The closest I've gotten is using the Brave Halfling Delving Deeper classes in one game and the Labyrinth Lord Advanced Edition Companion in another, and both of those are much simpler (or at least more simply presented) than the actual AD&D rules.
I think what I like about D&D is the simplicity of the core system — if I want something more complex, I'll probably go with another system — and the original AD&D books are just more complicated than I want from D&D. If I was going to run an AD&D module, something I'd have no hesitation to do, I might pull out OSRIC, but I might just use Advanced Edition Companion and not worry about the minor differences. Actually, now that I think about it, I might just use Swords & Wizardry Complete.
Something about D&D 3E and 3.5E brings out the min-maxer in me as a player, and prompts me to try to build NPCs like I'd build PCs and creatures using the official rules, with feats and skills, etc., but those rules end up annoying me through their fiddly but ultimately restrictive nature. It is worse than BESM, where at least the fiddly rules let you create almost anything.