my understanding is the opposite. neutrinos fill the universe similar to photons, they are just extremely hard to detect because of their weak interaction with other matter. So detections are rare, not neutrinos themselves.
a quick google estimates that a human has about 100 trillion neutrinos pass through their body every second, but only about 25% chance that even a single one will interact with any atom in your body over a lifetime.
it is a detection issue, not a quantity issue.
The situation with neutrinos is exactly analogous: IceCube looks for high energy cosmic neutrinos, not low energy background neutrinos. The latter are only of interest to dark matter searches.