If the rate freeze works, then the MBS investors will ask for high rates for their money, which will price even more people (even with excellent credit scores) out of market.
When even $150K income can not afford the $600K house, because of tighten lending standard and interest spread, the house price will goes even lower and over-correct……
The end result will be more default and more inventory on the market.
No matter what you do, the price has to go back to the norm. Better no bailout and let the market find its way out than having the bailout and blocking the most efficient way to the recovery.