A lot of hospitals rely on volunteers, despite being multi-million-$ nonprofits. My mom volunteered for one in high school and said it was one of the more rewarding jobs she'd had. Aside from the various work-experience and work-ethic things, she also learned how to make the bed with hospital corners, which my sister and I benefited from all our childhoods...
I'm coming to this mostly from my mom's perspective. She's a medical illustrator which means that hospitals make up a substantial fraction of her revenue, but she's constantly getting calls from "non-profit" hospitals that expect to be able to use her work for free. It just strikes me as disingenuous for a highly paid professional to be calling another professional asking for their services, and expecting to not have to pay for them.
I'm skeptical of a non-profit that pays a lot of professional people for skilled work, deciding that it isn't going to pay certain types of professionals for skilled work.