They could even charge slightly higher fees than most credit card companies just like AmEx does. They have the infrastructure in place via Apple Pay.
Since Apple Pay already supports the industry standard Web Payments API. They could convince more companies to accept Apple Pay on the web without being “locked in” to Apple Pay since if you implemented the payments API, it would also work on Android with Android Pay.
Apple Pay is an open standard that integrates with your standard credit card processing flow.