If you hold $100k in Bank of America (or a linked Merrill Edge account), they will give you up to 5.25% cash back for their credit cards in certain categories, and 2.62% unlimited.

https://frugalprofessor.com/bank-of-america-customized-cash-...

To your point, it's not free money at all: the credit card companies are collecting fees, and the merchants are passing them on to you. This is a way to claw a part of that back - if you don't use a rewards card, you're paying _even more_.