I dealt with athletic budgets in big high schools for 40 years, and the money involved is significant and hard to come by in the best of times.
HS Athletic Director? My dad was as well.
I was never the AD; taught and coached for 39 years. Basketball the whole time, tennis early in my career, golf late in my career, and a little bit of other stuff here and there.
So here's an example of financing issues, though we're talking about HS instead of college. For basketball, the county paid coaching supplements, bus drivers, gatekeepers and security, and game officials. EVERYTHING else, uniforms, basketballs, water bottles, towels, tape, and on and on, came out of school funds, which either had to be from gate receipts, privately donated, or raised through things like golf tournaments or Shoot-A-Thons or whatever. Some of this varies a bit from system to system, but that's the gist of it. The affiliation with a shoe company came along very late in my career, and it helped for sure, but that stuff wasn't free; it just had a far better price, plus the company threw in some shoes and warmups for the coaches as part of the deal.
Our athletic program budget was so tied to football gates that a season with bad weather on Friday nights, or a season where we didn't play our archrivals as home games, made things really difficult, and that was in a BIG metro system in a very affluent area.
Colleges aren't that different, especially if you get beyond the handful of teams that you see on TV year round in football and basketball. Everything else is a financial black hole. We all see the numbers of what Nike is paying coaches at the big time schools, but that has nothing to do with most sports even at those schools, and nothing to do with most schools. The vast majority of college athletic programs have more in common with high schools than with Alabama or Duke or UNC or Clemson or Kentucky.
One other thing to consider: Most of the programs that are currently being cut are men's programs, and I think in many cases schools have wanted to cut men's teams for some time, but colleges are doing this NOW because there is sort of a PR window open because of the pandemic. In addition to reducing their budgets, they are dealing with Title IX disparities. (I have no idea how Title IX applies to Brown, but I wouldn't assume that it doesn't apply if Brown is taking any federal money at all for any part of university operations.)
If there is another wave of program shutdowns, it'll come later after college AD's see the outcomes of 2020 football and 2020-21 basketball, plus impacts of the pandemic on giving. That's where the real crisis will come.