They don't make large profits otherwise they wouldn't be nonprofits. They do have massive revenues and will find ways to spend the money they receive or hoard it internally as much as they can. There are lots of games they can play with the money, but experiencing profits is one thing they can't do.
This is a common misunderstanding. Non-profits/501(c)(3) can and often do make profits. 7 of the 10 most profitable hospitals in the U.S. are non-profits[1]. Non-profits can't funnel profits directly back to owners, the way other corporations can (such as when dividends are distributed). But they still make profits.
But that's besides the point. Even in places that don't make profits, there are still plenty of personal interests at play.
[1] https://www.nytimes.com/2020/02/20/opinion/nonprofit-hospita...
Profit is money that ends up in the bank to be used later. Compensation is what gets spent on yachts. Anything spent on hospital supplies is an expense. This stuff matters.
Then where do these profits go?
https://en.wikipedia.org/wiki/501(c)_organization
"Religious, Educational, Charitable, Scientific, Literary, Testing for Public Safety, to Foster National or International Amateur Sports Competition, or Prevention of Cruelty to Children or Animals Organizations"
However, many other forms of organizations can be non-profit, with utterly no implied morality.
Your local Frat or Country Club [ 501(c)(7) ], a business league or lobbying group [ 501(c)(6), the 'NFL' used to be this ], your local union [ 501(c)(5) ], your neighborhood org (that can only spend 50% on lobbying) [ 501(c)(4) ], a shared travel society (timeshare non-profit?) [ 501(c)(8) ], or your special club's own private cemetery [ 501(c)(13) ].
Or you can do sneaky stuff and change your 501(c)(3) charter over time like this article notes. https://stratechery.com/2023/openais-misalignment-and-micros...
So yeah, Mayo Cinic makes a $2B profit. That is not money going to shareholders though, that's funds for a future building or increasing salaries or expanding research or something, it supposedly has to be used for the mission. What is the outrage of these orgs making this kind of profit?
Employees might suddenly feel they deserve to be paid a lot more. Suppliers will play a lot more hardball in negotiations. A middle manager may give a sinecure to their cousin.
And upper managers can extract absolutely everything trough lucrative contracts to their friends and relatives. (Of course the IRS would clamp down on obvious self-dealings, but that wouldn't make such schemes disappear. It'll make them far more complicated and expensive instead.)