There's room for both sides. It's nice to listen to something really well captured and with tasteful enhancement to make it sonically more interesting. Something, to me, like Natalie Merchant's Tiger Lilly or Nora Jones' Come Away With Me, those are all very good songs and very well captured and produced. That's one whole type of way to go about it and it works really well, and probably the exceptional capture does add something to it, even if not consciously to the non-technical.
But there's also the other side that works well, too. Probably each end of the spectrum works best for some types of music as compared to others. A rougher vibe is often very useful for some types of music, it's not even a compromise. It may be a conscious choice, e.g. Cobain's decision to make the music fairly primitive to offset the fact that he knew he was singing very 'pretty' melodies a lot of the time. And lots of indie stuff is purposefully done in a not overly polished way because it fits the aesthetic (though it may be that that aesthetic came to exist because most indie artists can't afford to do more and it just becamse the accepted sound of that sort of music.)
A really good engineer should in theory, at least on the good days, be able to get a good capture without unduly affecting the vibe or spontaneity. And some music just requires more thought, on both the band's and the engineer's part. Not everything is a three minute pop tune that can be put down in one shot, whereas a punk band may well only be able to get the right vibe that way. Some music benefits from time and care, Pink Floyd being a fairly canonical example for me.