The problem with lowering housing prices is that it would screw over everyone that currently owns a house.
No, the problem with lowering house prices is that it would be bad news for everyone that currently owns
more than one house (or has property-backed investments), has used the equity on their house to borrow money for other things.
The majority of people who own a house
need it to live in and, if they sell it, will need the money to buy another house. Even if they die and leave the house to their children, a major use of
that money is to buy a house or pay off a mortgage.
We saw this in the last housing crash where prices dropped and people owed more than the house was worth.
The flaw there is the one-sided way mortgages work, allowing the banks to rake in interest while the householder bears most of the risk of a property price fall - which leaves them free to promote irresponsible house price inflation by lending more money (oh, and then making
even more money by making loans to home owners based on their growing equity). That's bad even without the sort of insane money games that triggered the banking crisis. In that case, house prices
crashed across the board mainly because the banks panicked and stopped lending money.
You cure the housing crisis by increasing the supply of houses or reducing the demand by making rental more attractive (which it won't be when even the landlords don't own their property and expect tenants to pay their mortgage for them
plus a profit margin). Or price control (but that's a can of worms). Helping people get mortgages is just throwing more fuel on the fire by driving up prices.