> house prices [...] need to go down heavily.

As a layperson I have a feeling that's not going to happen. The working class has too much wealth tied up in their homes because US society and the government have encouraged people to treat it as a store of wealth instead of a box that shields them from the weather. People talk constantly about "getting on the property ladder", "buying more land because they aren't making more of it", "having a landlord side hustle", etc. A house is a lot more tangible than stocks so people without knowledge of finance feel much better about investing in one (understandably so - also forget about Social Security). Combine this with associated government tax subsidies and mortgage underwriting programs and you've basically created a situation where home prices can't do anything but go up.

Look at the amortization table for the proposed 50 year mortgage: borrowers wouldn't be making a dent in the principal for a good 10 or 15 years. The underlying assumption here is that people would make money via home price appreciation, i.e. speculation, not from creating an actual store of value. We already kicked this can once when the 30-year mortgage became a thing 60 years ago.

Of course one can't draw the current trend line into infinity because of affordability but I highly doubt it'll go down appreciably. I also don't know enough to have a solution to this problem - any ideas?

The uneven demographic curve shows that many elderly current homeowners will have to sell over the next couple decades due to death or moving into assisted living facilities. That will increase supply and reduce demand, although the impact will vary widely by region. Don't expect any major price reductions in popular areas but there may be further collapses in certain rural and economically stagnant areas. You can look at Japan for a preview of how that plays out.

Tax planning can help here. By converting the house to ownership by a tax-advantaged trust , a family absolutely can continue to extract rent from a former property without selling. Doubly so if the mortgage is paid off.

Sure, that can help affluent families in some cases. But many elderly people will be forced to sell (or reverse mortgage) their real estate holdings in order to pay for long-term care. Fees at decent assisted living facilities are often in the $8K per month range now so the only way to afford it is to sell the family home.