Also a good idea, but the details don't work out. Specifically, early on the Fourier components of the matter density distribution grow independently. Light neutrino DM would suppress the small scale clumping too much. Making the whole process last longer would fix this, but it would also enhance large scale clumping, contrary to observation.
It might be possible to make it all work out by adding a third effect (and maybe somebody has already done that!), but there's also a danger of constructing a Rube Goldberg machine -- if there are too many gadgets needed to get the structure right it starts looking like epicycles. The great thing about traditional dark matter is that it doesn't require any cosmological complications, it just works.
So lemme check my understanding here: are you saying that clumping has an observed size distribution, and if dark matter were just neutrinos, there isn't a timescale which would produce the clumping size distribution we see: if the timescale were short then we would see less small clumping than we see, if the timescale were longer then we would see more large clumping than we see?
It might be possible to make it all work out by adding a third effect (and maybe somebody has already done that!), but there's also a danger of constructing a Rube Goldberg machine -- if there are too many gadgets needed to get the structure right it starts looking like epicycles. The great thing about traditional dark matter is that it doesn't require any cosmological complications, it just works.