The US certainly has issues with even accepting the government being able to do good things. A small but highly vocal part of the populace has all but ensured the well is poisoned. I think we could, if we wanted, create an institution like the USPS for financial services. That would be able to issue a mortgage. It's not going to happen for the simple fact they're doing their best to privatize the USPS and beloved programs like Social Security.
The US has a good deal more public services than other countries; privatized mail, utilities and mass transit are all pretty common.
Mortgages themselves are unusually public in the US and probably staying that way. Other people don't get 30 year fixed loans, that's a huge benefit and inflation defense.
