Why haven't they done this on Android already? Why aren't my employers currently mandating that I install 3rd-party stores on Android phones?
Most Android users I know have never installed an Android app outside of the official Play store. Why haven't companies taken advantage of them yet?
You have the chicken and egg problem there. There are no apps so no users and no one is going to add apps because you don't have users.
Big companies could make their own apps to promote their own shop but let's be honest they would have to put a lot of money to get something good that everyone would use, not just generic crap.
I suppose this would mean that Facebook app itself would have to be sideloaded, which would probably result in a hit they wouldn't want to take. For a while Amazon had two versions of their app on Android, one in Play store and a second one you could sideload that had their app store integrated. Based on the fact that AFAIK they now only have standalone app store for sideloading, I assume it wasn't a popular option
People will install insecure app stores to get a hot app. Facebook would likely launch a store with none of Apple’s spyware restrictions. Cisco and IBM and Microsoft would too, and with that come e.g. employer mandates for certain apps and thus certain stores.
Apple regulates its App Store. Remove its distribution control and that regulatory power diminish. That diminish meant is fine when Apple extends its App Store dominance to win at music streaming and payments. But it’s a poor argument against the App Store per se.