The iOS App Store can easily become the desert the Mac App Store is today
Not really comparable: the iOS App Store has always been the
only way to install third party Apps on the iPhone/iPad and those Apps have always been rigorously sandboxed. It has a lot of momentum, and a huge catalogue, so any new contenders will face a high bar.
The Mac App Store was a late bolt-on, starting from scratch on a platform which already had a thriving industry supplying software on disc, via direct-from-the-publisher downloads or third-party app stores. Also, the sandboxing on the Mac App Store broke lots of existing apps.
The two problems I see with the App Store (c.f. other app stores) are (a) Apple's ability to act as judge jury and executioner when it comes to rejecting Apps, with the potential for allowing them to block anything they see as "competition" and (b) the inability to keep
usable backups of apps (...that don't turn into pumpkins if you change the Apple ID or want to install them on a new device after they've been withdrawn from the store). That said, (b) has to be taken in the context of reality where many independently-obtained apps require product activation that relies on the companies servers being up and running, and modern concerns about security mean that the days of running 10-year-old software may be coming to an end...
(a) is maybe where some legislation requiring transparency about rejections could help.
Let's just hope that the Powers That Be don't get distracted by the whole "Fortnite" thing - which seems to me about dodging Apple's commission by giving away your App for free, then using your own in-app-purchase scheme to make money hand over fist.
Or to put it another way "Hi, Mr Walmart - can I call you Wally? It's King Camp Gillette here - how'd you like to be the exclusive distributor of my free razors? What's that Wally? Blades? No, no, I'll sell the blades directly. <click> Wally? Wally?"