Currently we do not. There's been some of it on the fringes of enterprise/corporate stuff, but in the mainstream the Play store has had a de-facto monopoly for a while.
I would argue that this doesn't change my previous argument. I'm talking about how the "modern" OS experience necessitates a near-monopolistic app-store. That the OS cannot be separated from the app-store. This is also the current state of the Play store, even if google technically allows competitors. I also think their reluctant acceptance of these competitors was relatively recent, and therefore that market is still young. I would think that by the time several competing app-stores exist with their own exclusive apps, you'd have a markedly different experience on these OS's than you have today.
