I'm not sure that follows. Can you elaborate on why you would "lose that choice"?
Previously those apps were forced to make concessions to be on the iOS store, and I could download "Instagram, the version that makes Apple happy" app.
But now, that version of the app is gone! I google "Why is my Instagram gone" and get an article that says I have to sign up to the "EpicTwitBook" store, and download the "Instagram, the version that makes Advertisers happy" app.
I would prefer the first version but I don't get a choice.
My vision of an alternate app store still involves largely adhering to Apples rules for app approval. Except that an alternate store could have a different commission structure and in-store "experience".
For example, an alternate store could differentiate on search features, curation, free trials, ratings systems, bundles, periodic sales, developer interaction, developer support and (optionally of course) social recommendations. Exclusivity could even be forbidden.
In this scenario, Apple could still set the rules for App approval (with some oversight) and earn a fair commission (%5 to %10?) on transactions. It would still be profitable for Apple but encourage innovation and competition in the actual "stores".