You raise football back up 20 spots, you've now just cost another men's team their sport(s). I'm guessing that's right around the amount of players on a men's lacrosse team. Be careful what you wish for.
Yes and no. Warning... long winded post incoming.
It's really not apples to apples when talking about the financial impact of relaxing or eliminating scholarship limits. You're absolutely right that in a "free market" revenue sports are going to get the VAST amount of resources and scholarship money and the like. And there are many examples recently of schools cutting swimming/track/baseball/etc. from struggling athletic departments to save $$.
However, before the age of scholarship limits and such, there were plenty of non-revenue teams and there always will be. Then Title IX happened, which made each team effectively cost more than double. The truth is so few scholarships are used by non-revenue sports that the majority of the cost has absolutely nothing to do with scholarships and it isn't a sum zero game. There are many (if not the majority) of non-revenue teams across the country right now that don't even hand out the max scholarships each year because it isn't in their budget.
In reality, an increase in available scholarships would most likely mean reallocation of wasted funds in the football budget for most schools. Instead of the facilities arm race, bloated recruiting budgets, absurd amounts of direct mail, etc. they'd reallocate towards more scholarships. There would absolutely be some schools that go "all in" for football and scrap programs to reallocate more money... and I have no problem with that. If there isn't institutional support for the team and the admin wants to scrap it, then that's the way the cookie crumbles. No one should be compelled to field a team they don't want to field. The number of programs around the country that function just fine with no scholarships in DII or DIII or even DI shows you that you can easily field teams for lesser sports with no scholarships at all.
A good example of how things could go down is Maryland and Cal recently. Maryland athletic department had an absolute ton of teams they were supporting. They decided it was too much of a burden as the department was in the red.
So they cut a bunch of programs no one cared about and couldn't raise enough money to support. Not many shed a tear for water polo or acrobatics, which is why they don't exist anymore. Conversely, Cal was in a similar predicament. They announced they were cutting baseball, rugby, gymnastics, and women's lacrosse. The savings would be $4mil/year (the equivalent of 100 scholarships to ND... which shows you just how much of an operating budget for these sports is completely outside scholarship costs). People said "what! we love those teams!" and they got enough support/donations to keep lacrosse, and then enough to keep rugby, and then enough to keep men's gymnastics... and finally, enough to keep baseball and women's gymnastics. The point is that if a school should have a sport, then it will have a sport. And if it shouldn't have a sport, then it won't have a sport. The system self regulates if you let it.
There is also a whole separate debate to be had about Title IX that should be reserved for another thread, but is worth having.