I'm personally not a fan of such a situation but it's a reasonable one in today's world.
Seems like an easy fix for the case that's reasonable that doesn't require people to subsidize the wealthy.
The FHFA assesses up-front fees on second homes [1]. One could simply delay this assessment, for a fee, and not assess it if e.g. a year down the line the borrower only has one mortgage. (That said, it seems simpler to reduce the threshold to two from ten.)
[1] https://www.fhfa.gov/Media/PublicAffairs/Pages/FHFA-Announce...
Not a fan even in today's world. Example:
The house next to mine sold for $300k 2y ago. Those owners put about $50k into renovations and sold 1y later for $450k. The current owner did nothing (didn't even mow the lawn!) and 6m later decided to pack up and move across country for a job. He put the house on the market for $650k. It's beyond insulting. That house is going to sit on the market for a long time unless he is willing to make no money or even lose money on the overall transaction.