For me, the amp produces a sound/tone (plus air, and whatever else you feel like adding) - especially in terms of low end - which so far hasn't been duplicated by any DI I've ever heard. I guess you could make the same argument that the reverse might also be true; that no amp sounds like a DI.
However, since I spend 99% of my time outside the studio or stage playing through an amp, by comparison the DI alone tends to sound a bit sterile (IME - for lack of a better word). Plus, I've had the opportunity to tweak the settings on my amp quite a bit (if not to death) in a variety of different sized/shaped rooms. I personally don't get to do this when it's a DI into someone else's board.
However, since I spend 99% of my time outside the studio or stage playing through an amp, by comparison the DI alone tends to sound a bit sterile (IME - for lack of a better word). Plus, I've had the opportunity to tweak the settings on my amp quite a bit (if not to death) in a variety of different sized/shaped rooms. I personally don't get to do this when it's a DI into someone else's board.