Would Valve not rather have Microsoft than Google then? Windows users have administrator accounts and can install steam and its games without issue. Google play store would directly compete with steam.
Google exerts a lot of power over Android.
The EU did recently punish Google for that, so theoretically Google now has to stop with it, but up until this point, they forced manufacturers to only ever preinstall the Google version of Android (or permanently lose their license to preinstall the Google Apps) and also forced manufacturers to always install the whole Google app bundle, not just the Play Store.
To put their power into perspective, just remember that Amazon has been in the game of distributing an Android fork and alternative app store for a while now. And Amazon is magnitudes bigger than Valve.
It was easy. They just started using the same name, “Android”, for loads of proprietary stuff, and the geeks didn't care because they were too busying sucking up to Google for not being Microsoft.
I believe Lineage and co have to supply their own replacements for some important features, and/or use the proprietary Google Play Services.
AOSP isn't a usable base product, like Chromium for example.
(That's my understanding anyway. It's quite possible I'm wrong!)