Every non-stock app on my phone was installed from an APK directly downloaded from the manufacturer or open source developer's site / Github releases. I've never had a Google Play account and have never used any Android "app store".
The biggest pain was having to manually logon the couple of sites I allow to keep persistent cookies since device owners aren't allowed to just import/export cookies from mobile Chrome.
It has been a very nice experience. I appreciate the feeling of sovereignty and ownership of my device (even though it does have a locked bootloader and I don't actually have root).
Of course Google would take this away. >sigh<