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:
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.
*Maximizing the Technological Capacity of New Zealand in Post-Catastrophic Isolation*
I've been considering a project which would aim to maximize the technological capacity that New Zealand could maintain were it isolated following a global catastrophe.
I've written a one-pager, discussing why the project is of global importance and providing a little more detail as to what the project might entail.
Would be happy to receive any feedback or to answer any questions :)