Developers can absolutely develop an app with whichever payment system they want and keep all the income to themselves. Develop a web app and do whatever you want. You integrate with whichever third party systems you want and provide the experience you think is best for your users and yourself. Anyone will be able to use your web app from an iPhone as much as they will be able to use it from a Desktop device.
However, if you actively choose to develop a native iOS app in order to integrate with Apple's native APIs in order to provide an experience which can be superior to a web app then it's not a far stretch to expect you to therefore integrate with Apple's native APIs across the board, including payments. I mean that is literally why you choose to develop a native app, because you want to provide EXTRA value to your users by making use of APIs which Apple invested in.