How many of those apps actually run without Google integration, though, and how many will continue to in the future? Google's moving more and more core functionality into their proprietary components.
If you look at the dividing line between proprietary and open source stuff coming out of Google, the usual deciding factor is whether it relies on their (proprietary) server side components to operate. Google is all about the cloud so a lot of useful stuff does rely on that. In Play services we see things like Maps (needs the servers), Wallet and in-app billing (needs the servers), G+ (needs the servers), multiplayer gaming (you get the idea), GDrive, ads, cloud messaging etc. There's one or two things in there that maybe don't rely on the cloud (I don't know enough about Cast to say) but that's mostly it.
So if you find all your apps are relying on Google Play Services what it really means is that the bar has simply been raised, and now people expect apps that deeply integrate with services provided by huge, expensive datacenters.
Ideally Play Services would be a shim that different providers could satisfy. It isn't, but Android has lots of support for building such things like intent resolution, so if a realistic competitor emerged and developers cared enough to support it, the OS would certainly help them.
In the end, I think it's a good thing that AOSP doesn't have a dependency on some cloud service, be it Google's or someone else's. The unfortunate downside is that developers might forget that the cloud service they want is not available.