There is currently a sperm donor shortage in Britain, which they feel was brought about because children resulting from such procedures can now know the identity of their donors.
I'm guessing none of these kids can ever sue their fathers for child support ever, but I guess the possibility of some kid knocking on their door after twenty years isn't worth the trouble of giving a cupful of spermies. Then again, why donate sperm if you'd be weirded out that it would become an actual human being someday?
And I really think children have a right to know who their biological parents are. After all, they pass onto you their physiological inheritance and biological limitations. And indeed, what if you hook up with someone you're biologically related to? Case in point, twins parted at birth who got married in the UK.