I doubt that paying a middle-class psych to run experiments will do much to improve the lives of homeless.
That said, a lot of homelessness happens as a result of mental illnesses like drug addiction or schizophrenia, or degenerative diseases like Alzheimers. It might be a pipe dream, but I would like to have as much research as possible to help treat these diseases, to (hopefully) help reduce these issues, perhaps by developing a cheap medication to reduce or eliminate the effects.
It's not something any of us are immune to; any of us could develop Alzheimers when we get older. I'm fortunate enough to have a lot of really cool friends and family that would take care of me if that happened, but not everyone is so lucky.
Those with mental illnesses who are also homeless are more visible, but the majority of those who are homeless are homeless because of financial reasons. And often, they're entire families.
For NYC[1]:
> Research shows that the primary cause of homelessness, particularly among families, is lack of affordable housing. Surveys of homeless families have identified the following major immediate, triggering causes of homelessness: eviction; doubled-up or severely overcrowded housing; domestic violence; job loss; and hazardous housing conditions.
[1] https://www.coalitionforthehomeless.org/basic-facts-about-ho...