I personally see the MBS market as a small problem to the federal government for a few reasons:
1. Most homeowners are in a rather comfortable equity position meaning the draw down in the market would need to be ~40% or greater for the creditor to not be made whole even in the event of a foreclosure.
2. There would be MUCH bigger problems prior to housing market going down noticably, ie stock market returning to just a historically normal valuation would crash the economy and tax receipts and lead to a debt financing issue (if liquidity is sucked out of the system there's no money to buy the treasuries.)
Even if house prices feel inflated they've got nothing on stock valuations:
https://www.longtermtrends.com/stocks-to-real-estate-ratio/