The argument hinges on Google not owning or operating Android. AOSP has been a dead dream for a while now due to carriers locking down phones and Google needing to circle the wagons.
As you mention, AOSP alone does not give you much Android and Google is likely to dictate all kinds of terms to use the Play services, Play Store, etc. So, the question is indeed does AOSP give enough to argue that Google does not fully control the Android market.
Personally, I am not sure this is the most problematic aspect of Android though. If we assume for a moment that Android is a near-monopoly in the EU, the more troubling aspect is that people can only choose between having no smartphone (which is becoming harder) or letting Google suck all kinds of data out of them. In other words, only when you are rich enough, you can afford not to let a company suck up a lot of your private data.
There are still a couple of european countries where iOS devices sell extremely poorly. I am not sure if this is because of an absence of subsidies or another reason.
Even if Android is the only option, you can always choose to refuse all data sharing from google, you are not forced to create a google account or to use google play.
Admittedly, it makes things harder for a neophyte.
That's only in the US.
Let's be honest here, AOSP is a dead dream because porting and maintaining AOSP for a device is kinda complicated. Many people do it for free, but you can't rely on that.
GPS includes stuff like location services, Firebase, Chromecast, analytics, Google account authentication, Google Drive APIs, all the game stuff, Android Pay, etc.