If mortgage rates are decreed to be cheaper than what the market would otherwise demand, somebody needs to bear the risk. The risk cannot be made to go away by any form of hand-waving by the government.
Freddie and Fannie were lucky for many years until they rolled a "7". They were a way to hide the risk (they were very complex organizations, hard to understand), but the risk was always there. Because they were so large, everybody knew that the taxpayers ultimately would be on the hook.
If Freddie and Fannie are abolished, the risk will be formally placed on you and me as taxpayers. But it has always been there--the taxpayers got lucky until 2007.
This is the real issue--how should our economy absorb the risk of mortgage lending. Coming up with the best answer will not be easy. This is particularly true if the profits made in good times are allowed to be separated from the losses in bad times.