” will the removal of the Government guarantee (as is the suggestions) really provide incentives to ensure the underlying loans are good?”
Of course it would. As long as you didn’t replace it with another govt guarantee, like a govt guarantee against bank losses if banks take on the risk.
But this misses the whole point of FNM and FRE and FHA. They are there to funnel money into housing demand, to make home prices higher than they would otherwise be. Since most voters own homes, and most voters really want to see their home prices high, not low, pols direct various institutions to do things that increase house prices. If they pulled the guarantee from FHA loans, pols would replace it with something else. If they didn’t, home prices would really collapse, and voters and banks would besiege Congress.