It's tricky because there's not really a great alternative to creating the Play Services divide because those services are pretty integral to how a lot of apps function and they rely a lot on outside data and servers so you either have a separate bit of the OS handle it or you have base AOSP have weird dependencies on Google servers for data.
Also I think a lot of the movement of things into Play Services instead of the base OS is because manufacturers were so horrible about actually updating their devices so Google moved it out of the OS into a portion they could actually control so they could actually roll out updates in a timely manner.
First of all, Google is responsible for poor updating of devices. Don't blame anyone else for the fact that their OS is hard to update, and Google doesn't require even basic security fixes as a requirement of getting the Play Store. (If you're unaware of what the MADA is: Google actually gets to approve or veto every device and software update released for devices running Android, effectively, and uses it to make demands about installed apps and branding.)
Second, the OS, designed for openness, would have open protocols for apps to build on that could be backed by anyone's servers. For instance, you can add multiple location providers to Android, there's no excuse for telling developers to build a dependency specifically on "Google Location Services". An open platform would have the location provider in the open source OS, and then apps would pull from whatever location services happened to be on the device in question, whether that be Google's servers, Samsung's servers, or someone else's.
The reality is that Play Services was designed for one purpose, and one purpose only: To create a proprietary fork of the Android application platform that would only run on devices Google controls via their secretive contracts with manufacturers.
I honestly don't know why this is downvoted, I pretty much agree with everything here. The current situation is pretty much a result of politics and policies, not technical issues which can't be solved.
I'm not so certain that's exactly how it'd go. OEMs faced with being forced to provide updates at an unknown pace might just decide to try to roll their own version of Play Services and the underlying data that those hook into, which given the quality of their normal bundleware isn't too promising.
Play Services are mostly necessary for commercial apps (to show advertisement, so spy on user, to collect payments). Many applications in F-Droid do not require them.
And using Play Services doesn't require to have an account with Google or to have a network connection. As Google Play Services are distributed for free, anyone can download them and set up so that they cannot connect to Google but still allow to run apps dependent on them.
Also I think a lot of the movement of things into Play Services instead of the base OS is because manufacturers were so horrible about actually updating their devices so Google moved it out of the OS into a portion they could actually control so they could actually roll out updates in a timely manner.