You're mixing up various concepts of security, and that - in general - just doesn't work.
First, universal hashing on its own does not have any security property. Universal hashing is used in some constructions, for example UMAC.
Secondly, you used the term GHASH, which is an internal function of GMAC or GCM. The security property holds for the entire construction, and you can't just take one part of it. Then you use that next to Poly1305, which is in fact a MAC, so it's quite unclear what you actually meant. And then you call them hash universal hash functions, which is again something different than a MAC.
And thirdly, if a construction is safe with a certain function $f$, then you can not translate any security property to a generalization of $f$ without a proof. A simple argument for that: Regardless what $f$ is, a generlization would be "just any function $f'$". And that always includes $f'(.) = 0$, which is not useful in almost any case.