I think you are again confusing the nature of the marketplace. This is not about the cell phone marketplace. It's about the app store marketplace.
If you want to get an app to smartphone users, you have no choice but to list your app on Apple's App Store and Google's Play Store. There are no other ways to reach the vast majority of smartphone users. You, the app developer, do not have a choice. You have to suck it up and live with Apple and Google's policies, you can't take your business elsewhere if you don't like it.
So no, Apple and Google do not have to compete to attract developers to their platforms. Their terms are equally onerous, almost as if they colluded to keep prices high.
Or maybe, just maybe, they both looked at the costs of maintaining their App Stores, Approval Processes, and Payment Processing, and came to about the same conclusion regarding a reasonable Commission.
And no, I'm not confused at all. Android allows Sideloading; therefore, a reasonable Consumer has a Choice, and so do App Developers. Too bad the old independent software distribution model isn't seen as more desirable to most Consumers; that's simply Market Forces.