I’d be more than happy to use a secure, fraud-safe payment system that does not give me airline miles if it meant everything was cheaper to begin with. Part of the problem with CC companies is they do many things that are tightly coupled and are positioned well to profit on them.
The problem is the ‘fraud safety’. Your ‘safety’ is likely to be some else’s inconvenience (or vice-versa), and credit cards are all about ease-of-use. Fraud-related costs are also one of, if not the largest single contributor(s) to payment processing fees.