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".

I switched from iOS to Android about three years ago. I saved all the APKs for everything I installed (or updated). When I got a new phone last fall it was pleasantly like geting a new PC. I imported my SMS and contacts from my last backup, then installed all the apps I use and imported or manually set any settings I wanted to customize.

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.