The Santa Fe Institute is an example of what I'm suggesting at the end of this comment. https://www.santafe.edu/

As a PhD student in economics, I'm skeptical that funding a "welfare economics" department would actually change the research outputs of universities:

1. Pretty much all economic research could be called "welfare economics", so (without further stipulations) a funder couldn't point to a specific project and say "Umm that's not the sort of thing we want".
2. Economists are fairly insular, and I can't see a department ran by economists hiring (e.g.) crop scientists or AI engineers (I'm an economist so I'm allowed to say that). Rather, I think economists would hire economists, who would probably do the economics they would have done in other jobs.
3. While I'm not 100% sure how universally true this is, my sense is that funders (rightly) have limited control over the departments they fund. That's been my experience as both a predoc in a well-funded lab and as a PhD student.

I agree with other commenters that "wellbeing science" is maybe a better fit. I guess "environmental science/studies" departments are probably the best model here.

That said, my sense is that this would be a low priority either way. Universities have pretty high overheads and are pretty inefficiently run. It would probably be easier to set up independent think tanks. If you wanted to influence curricula / academic conversations you could perhaps do so by giving part-time fellowships to individual professors.

N00b question-- why do people have to apply to EAG etc? All of the academic and political conferences I've attended have let anyone attend (with the exception of people who pose a safety risk). What's the role of gatekeeping here?