The economics of it isn't just handing you your own money with a couple arbitrary hoops in the way. There's a portion of cross-subsidy from cash, debit, and low-rewards credit card payers, along with capturing some of the merchant's efficiency gains of using cards over cash (harder for employees to steal, no need for armored cars for cash pickups, etc).
I think you would be surprised at how little cash many places need to operate with in the presence of credit cards.
Consider a front desk at a hotel. Thousands of dollars a day in transactions occur via card, which would warrant frequent drops into an expensive safe if they happened with cash. With cards they pretty much only hold a trivial amount to deal with sundries that isn't worth protecting beyond a simple envelope to a back-office.
Credit cards dominate many industries in the US to a point where cash management is now trivial because the daily amounts aren't worth any employee losing their job over or a criminal risking robbery punishment for.
That hotel is still doing cash accounting though. If there isn't much at the front desk, how about the bar? The restaurant?
A business that has any type of daily cash accounting is still going to need to balance the register at the end of the day, reestablish change to open with, have arrangements for transport, &c. Bad employees can still pocket a tenner on occasion.
Sure, some smaller places with barely any cash probably just lock the drawer and call it a night.
I can't find the figures now, but estimates of cost of cash handling is far far lower than the 2-3% of swipe fees.
If you put down your loss due to clerical errors, theft, etc. of handling cash at around 1%, increasing the amount of cash will also increase your loss. Credit cards and other electronic payment methods, won't have that issue.
Not really. Banks really dislike creating systems where it is possible for them to lose money. And by law, if you pay your credit card statement in full on or before the due date, you get charged zero interest.
The interchange fees charged to merchants roughly covers rewards. It's why Visa et al charge higher fees to merchants for processing higher-tier rewards cards. Interchange fees don't cover all the other overhead of running a credit card system, but they do cover rewards.
Interest payments cover the fixed costs of running a credit card system (and then some). Payroll, marketing, offices, return on capital, etc. An additional marginal purchase usually generates enough in interchange fees to cover the rewards earned on it.