I think they're a distraction. Wargaming is a hobby unto itself. So is crafting and detailing figurines. Neither of those has anything to do with roleplaying. I'll occasionally use a grid for complex battles with whatever's handy as markers, but I hate doing that. The goal is for everyone to imagine what is happening. On that level, miniatures are a crutch, and like a crutch they are not conducive to normal utilization of one's ability.
I also find that the grid takes a lot of time, and encourages a certain metagame tactical approach. The character does not have a bird's eye view of the scene. He should be making a snap decision on limited information, not plotting his next move like a chess piece. I'd rather play fast and loose and get to the parts I want to rather than worrying about exactly how many feet everyone is away from each other.
To top it off, miniatures cost money, and a large part of the attraction of this hobby is its inherent independence from financial considerations. They also take up space, and are frankly an eyesore. I wouldn't want to bring guests to my place and have them see a giant collection of little figures.
I never understood what the upside is of using miniatures in a D&D context.
As to the "purist" idea, I know that D&D and miniature wargames have a shared heritage and I understand why people have tried to use them. So I don't think that D&D sans miniatures is more "authentic" or anything. Having tried myself, I just think the game plays better without them. I look at them as an anachronism. No one would say that tennis with wooden rackets isn't real tennis, but we're kind of beyond that now.