Unfortunately no one will start their own store because that is huge investment.
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.
If a big company (e.g. Facebook) integrated their app store within their main app, there's automatically a massive userbase available - it could potentially even slightly streamline the install process for apps advertised via Facebook.
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
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.