Of course, it's also possible that colleges will find other ways to pay for the "lesser" sports, and there would be no cuts.
How much 'funding' does an amateur university sport need? I don't think my fencing club at university had any 'funding' we just met and fenced. Occasionally we borrowed a van to go to a competition. We had a coach we paid from a few pounds of membership fees we collected from ourselves.
- equipment
- coaches
- travel/hotel/per diems, sometimes long distance depending on league
- trainers
- workout facilities (typically shared)
- practice facilities (might be shared)
- game facilities
- additional dining options to accommodate training
- nutritionists
- doctors
- scholarship money for tuition
- scholarship money for room and board
- video review areas and equipment (shared)
- video recording equipment and videographers
- insurance
- announcers for events
- recruiting
- tutoring
- event management
- publicity/advertising
- title ix compliance official
Note that at some universities (even some high schools), there are self-funding booster clubs that will pay for a lot of this stuff for some sports. That said, there is still some stuff that the university has to pay for directly.
As a simple example, Alabama football (big program that makes tons of money) also funds Alabama’s championship teams in golf, softball, and gymnastics (and many other sports that have not led to national championships).
(Source: I played on my college club kendo team. If anything the needs of fencing are less than those of kendo.)
Most "rec sports" are self-funded university-affiliated student clubs. I was the treasurer of one such club for three years.
My school's cycling team ran about a $20k-$25k/year budget to cover race transportation, motels, entry fees, coaching and an annual 2-night training camp. That was for a full collegiate road season with an average of 6-8 riders and about 75% of a MTB season with 2-3 riders.
Funding came from sponsors (mostly selling space on the team jersey), selling jerseys and bibs to alumni and donations. Most of the sponsors were alums with local businesses, but we also had a couple bigger brands (energy bars and cycling clothing) who gave "in-kind" donations of steep discounts on merch (>50%).
Team members paid for their own equipment. We did discuss buying a couple team bikes to bring in people who could not afford them, but budget constraints and concerns about damage/jealousy/competitiveness nixed the idea.
I'd guess that you could run a competitive "varsity" cycling team, including everything I mentioned above plus mechanics and equipment but excluding scholarships, for around $40k-$50k/year (assuming mechanics are paid a day rate at races and piecewise for maintenance and the coaching staff is not full-time university employees).
First college enrollment is likely going to drop significantly starting around 2025 due to severely declining birthrates in the US that started during the 2007-2008 financial crisis. It is expected that 2025 will be the smallest graduating high school class in the US in the last 30-40 years. Every college and university is going to be fighting over a smaller pool of applicants. Fewer people are going to attend games and fewer people will be watching college sports on TV which means smaller TV contracts.
The percentage of men attending college has been declining, in 2017 57% of college students in the US were women: https://nces.ed.gov/fastfacts/display.asp?id=98
And it looks like the declining rate of men in higher education is only speeding up: https://hechingerreport.org/the-pandemic-is-speeding-up-the-...
College men and male alumni disproportionately support college athletics, they attend games and donate to the athletic department more than their female counterparts. Fewer men on campus in the long term likely means less money for the athletic department as a whole: https://onlinelibrary.wiley.com/doi/abs/10.1002/nvsm.34
Lastly, Title IX only requires that sports opportunities for both men and women be proportional to the percentage of men and women in the student body. With only 43% of college students nationwide being men now, and football being the juggernaut of college athletics that it is (with typically over 100 players on a college football team), there will be little room left for any other men's sports in college athletics, and no incentive for the athletic department to keep them around.
Over the next decades many men's sports will likely become nearly extinct at the D1 level: tennis, golf, rowing, wrestling, hockey, volleyball, swimming and diving, cross country, even track and field and baseball look to be in big trouble as athletic departments try to keep the revenue from college football flowing in while dealing with these challenging demographic factors.