That would open a can of worms regarding egg donors legal rights though.
I'm wondering if this would not be a good thing though, and similarly for sperm donors. We have gone down a bit of a rabbit hole with these things because it's been done in a piecemeal way, often to catch up with technology or sometimes new social practices, rather than with a clear vision of the purpose of recording this stuff at all.
As far as the father being recorded as such even with a sperm donor, that's really a quirk, isn't it, rather than something intentional? Husbands are always assumed to be the father unless someone says otherwise, because are you going to genetically test every infant? It just makes sense to assume that unless the mother says it was the milkman, or the father does, in which case these days there might be genetic testing.
Because of that very practical practice, even if there is a sperm donor the father's name goes on the certificate. But that's not the purpose of that way of doing things.