Unfortunately it's far more complicated than that.

Many of those people who own homes aren't rich themselves. If you look at the income distribution in the US you'll see that (even if we make the assumption that only the richer people own homes) homeowners could be earning as little as $50k, for their entire household. Only about 15% make over $200k. For the rest, if their homes don't do well as an investment, they're absolutely screwed as they get older.

I do notice homeless people but it's not a good way to estimate homelessness rates. Depending on where you are, that's likely to wildly over- or under- estimating homelessness. Some cities effectively have policies of moving homeless people to less visible spots, either through sheltering or though relocation. That's part of why people think SF has a rampant homelessness problem even though NYC actually has a hire homelessness rate. Homeless people also tend to congregate in certain areas for a variety of reasons (winter weather is a big one). Homeless rates in the US have stayed pretty steady over the last few years. https://www.huduser.gov/portal/sites/default/files/pdf/2022-ahar-part-1.pdf Globally the US is on par with many countries that typically go through a lot of pains to protect citizens rights; eg Germany, Austria Denmark, the Netherlands.

I suspect that the bigger effect is under housing. That is, people staying in homes that are no longer suitable for them.

The upside is that there's a very simple policy that is highly likely to have an enormous impact on all variations of housing shortage, build more houses. Credits and incentives only shuffle around the existing stock. Housing vacancy rates are near historic lows. Fix that and house prices will come down. A lot of people don't like that plan because it seems to capitalist. But, as I said at the beginning of all this, we would then need to find a way to help all the people who's retirement plan we just nuked. There are fairly straightforward ways to do that too. A lot of people will hate those plans because they sound too communist. My best guess is neither will happen and we'll keep plodding along with the suboptimal status quo.