This would not be a reasonable compromise, as one of the primary reasons for wanting competing app stores is because of Apple's insane overreach in trying to control what you are and aren't allowed to run on your own phone.
When I last had an iPhone, I wanted to install a heavy computing application that I had previously used on Android. I found out from the developers of that application that they had been rejected from the App Store because their app used too much CPU power. Apparently you're meant to just use the phone for decoration?
Google has some similarly nonsense policies (good luck finding a good adblocker on the Play Store), but at least it takes all of five seconds to circumvent that. Apple allowing competing app stores while still having complete control over the content available on them does very little to solve the problems that their monopoly causes.
Couldn't Apple offer a reasonable compromise that they only allow competing App Stores on their phones if those App Stores don't allow exclusive apps? App stores would still be able to compete on prices and payment methods.
I suppose that all apps would still have to be approved by Apple, though, otherwise an app creator could just hide something that Apple objects to in their app somewhere, causing it to be disallowed from Apple's App Store but allowed in third party ones.