Instead of paying those loans off why can't the government encourage this behavior like they do others? Tax breaks, gifts like this loan payoff thing, but to 2 parent families etc. Would probably be much more cost effective too.
However, I do remember when the Republicans tried to do it in the 80s/90s with the family values thing and got laughed out of the country.
Your last paragraph is what's going on IMHO. Biden buying votes, nothing more.