With that mindset, only the children of white, heterosexual couples should do anything that puts them in front of the public. When you're a single father, the question of "who's the mom" is bound to come up, so being transparent about that up front is probably better than having to address it when someone else uncovers the facts.
Plenty of celebrities strive to fiercely protect their privacy. Not every question needs to be answered, especially about a minor. So, it's a false choice (to either not become famous at all, vs. to share every little private detail with the public).
For whatever reason, a choice was made to announce Alyssa's parentage details on national tv to millions.
It just occurred to me - maybe extra publicity was encouraged by USFS, as a way to make sure Alyssa doesn't switch to China? (The Chinese state used to have some weird one-child policies, about controlling their population reproduction. So who knows how they will view her story.)