That's a perfectly good question, and that's exactly why for a time in the 90s they were one of the leading candidates for dark matter. Unfortunately it fell apart when we got a better understanding of structure formation, which determines the large-scale distribution of matter in the universe today. If the 3 neutrinos have masses around where we think, then they'd be too light and move too fast in the early universe, smoothing the distribution out and thus suppressing small-scale clumping, contrary to observations. On the other hand, if the 3 neutrinos were a lot heavier (possible we can only detect their mass differences, not the absolute masses) they would screw up the CMB. The qualitative case was great, but quantitatively it just didn't work out.