In the US. Not in Europe because interchange fees for consumer cards are capped at 0.3%

Yes that intuition is correct, though the reality is much more complicated. The actual share to the bank is roughly proportional to the risk of the transaction/ tied to the type of credit card

https://usa.visa.com/dam/VCOM/download/merchants/visa-usa-in...

US Bank for a brief period opened up a 4% card, but then closed it so quick that obviously the numbers didn't work out there.

2% seems to be a local maximum of cashback cards. There's a lot of 2% cards, and only a handful above that.

Makes sense?

2% is just an example figure, the actual rate varies