Spend the billions on F and F a different way?

Reader OSO has a slant on Freddie and Fannie:

As far as I can tell, GSEs of the size and purpose of Fannie and Freddie
are missing from more “socialist” economies than the US. It seems that
they are an aberration in both free-market economies and social democracies.

The nationalisation of Freddie and Fannie was not the best solution. A
better solution would have been to spend the same amount of money on a
one-off universal mortgage payment. This would be in the form of a
voucher sent to homeowners who would then use it to pay off a
significant amount of their mortgage debt. This would have helped
prevent many foreclosures, helped banks remain solvent and would have
eventually found its way into benefiting shareholders of Fannie and Freddie.

The first question is – why did the US even create these monsters? Yes,
yes, their basis was in The New Deal, which, to all pro-market Americans
means it was doomed to fail. But, even from a Social Democratic point of
view, the creation of a government sponsored enterprise (GSE) that
dominates an economy’s mortgage sector by guaranteeing loans is rather
weird. I might be wrong here, but as far as I know, no Western nation
with a more leftist economy than the US (ie all of them) has similar
Of course such a bailout means that the government has taken upon
themselves massive amounts of debt, along with having to buy the
shareholders out. I don’t know exactly how much money this is going to
cost the federal government, but it is a substantial amount and will
significantly add to the amount of net public debt already in place. But
I can’t help thinking that there could have been a better solution.
Instead of spending all this money to keep shareholders happy, why not
divide the money by the amount of money all people owe on their
mortgages and then grant them a once off government funded mortgage
subsidy, an amount which will be proportional to the amount they owe in
their mortgage?

In simple terms, this would mean that all borrowers would receive a
voucher from the Federal Government that they would then mail off to
their lenders – the effect being a reduction in their total mortgages.
That influx of money would not only prevent a whole swathe of ordinary
Americans from foreclosure, but, as the money circulates, would also
help prevent some banks from closure, prevent some mortgage companies
from going bankrupt and, of course, help Fannie and Freddie’s bottom
line. Rather than throwing money at the shareholders, the Federal
government could have helped ordinary homeowners and the entire market
that depends upon them.
To be honest, I’m all for Fannie and Fred’s closure. Whatever good they
were able to achieve in the mortgage market can be replaced by private
enterprises, better rules and regulations and the enforcement of such
regulations. The death of Fannie and Freddie will not ruin the mortgage
market, but will hopefully make it leaner and, hopefully, less subject
to overspeculation and investment bubbles. The intention behind the
creation of Fannie and Freddie is not to be questioned, but the results
must be.