My understanding is that the "certain Google proprietary apps" most importantly contain the Play store. Yes, in theory you could install FDroid - however if you, as a manufacturer, don't want to break the "install our app" flows of basically every website, you need the Play store - and therefore you also need to install Chrome, default Google Search and never sell a phone with Lineage OS installed ever again.

Not sure if the same licensing also applies to Google Play Services - if yes, this might make it difficult to even run the apps without getting the license, no matter which store is used.

Google have left themselves open to this.

1. They should release a heavily locked-down version of Android, which manufacturers and carriers cannot modify - apart from basics like bundled apps, widgets and wallpapers (uninstallable). Update would come direct from Google, and hardware support would be limited to specific components.

2. Make all of Android closed source and shut down AOSP. What is the point of it anyway?

This would solve the fragmentation problem, and be better for consumers since they would get updates quicker and for a longer time. Paradoxically it would lead to less 'choice' for consumers.