If you take a cash advance for $50 you only see $50 on your statement and the network doesn’t get its cut. If there’s no penalty for using a cash advance you’d find many businesses would have an in-house ATM so you could pay in cash and they could avoid the cost of accepting cards.
You actually see this in places like New Zealand where we have unregulated credit/debit card interchange rates but also have an established fee-free(ish) card system. Almost all smaller retailers accept EFTPOS card transactions but not credit/debit cards.