The argument you usually hear for why the government should guarantee mortgages is that commoditizing the assts without risk of credit losses will make them highly liquid and cheaper for borrowers to attain. Some may find that a compelling reason, even though taxpayers just cover that risk premium instead of the borrowers. But the real foundation for the federal government must guarantee mortgages stems from a deeper concern: when a recession and credit crisis hits, the mortgage market could close down entirely. So even if you're okay with mortgages becoming more expensive, is there any way to eliminate the government guarantee without risking periods of time when no one can get a mortgage?
Let's consider the most recent example of a credit crunch: the financial crisis. Despite the securitization market closing down and banks struggling to get cash to lend, the mortgage market remained open. One reason why was precisely what advocates for government guarantees would cite: the GSEs continued to provide funding for and back mortgages. As a result, the market kept on chugging along, albeit it at a slower pace.
But this wasn't the only factor. The Federal Reserve also purchased over a trillion dollars in mortgage securities. Why not ensure the mortgage market will stay open by relying on the central bank to step in during a credit crunch and perform this function when necessary?