I am curious if colleges/universities have bank accounts with consumer banks such as Chase, Wells Fargo, etc. I wonder this because, while colleges are a business, they are not businesses in the same sense as restaurants. Most of them are non-profit, and they typically are publicly funded. If you in the financial section of a college/university, then I am curious to know.
No business, non profit or otherwise, can really operate without bank accounts. How would they pay employees, professors, vendors? What would they do with your tuition check? Large universities avail themselves of more sophisticated business banking services, too, like sweep accounts, lockbox payments, etc. Sometimes banks are used for those cards where you load cash at college.
Being a non-profit is a tax designation. It has nothing to do with the daily handling of receivables and payables, which require bank accounts.
So? All non-profits have bank accounts too.
Some colleges might have some of their liquid assets in their own credit union as opposed to a bank, none just stick millions of dollars in their vaults; they’ll maintain enough cash on-hand to get through the day’s (or a few days’) cash transactions.
Any organization that uses money in any capacity has a bank account.
Translation: ALL of them.
Well, all legal organizations. 
This is an odd question. Curious why you would think a nonprofit or an institution that receives public funding wouldn’t have a bank account. What about your local public schools? Museums, government, libraries. Where would they put their operating funds?
What’s the reason for this question?
How do you expect a school to pay bills or pay employees? What do you think happens to your tuition and fees. Of course, they have bank accounts.