People don't know how opt in to beta.(I still don't after reading that page). Also requiring Google Play excludes open source android users, users on devices without Google $$$ licenses, and users who decline to link their device to a Google account.
That page is for developers, not users. Opting into beta for an app is pretty straightforward - users just need to join a beta community/group and click on a link to opt in. (I run a beta community and users haven't had any practical problems to my knowledge.)
Your points about open source Android etc are valid, though note that the beta channel will auto-update on each update (if user has auto-update app settings), whereas sideloaders will have to manually update it all the time. If you're releasing fast and frequent, it's unlikely testers will want to go through the manual install process on each release.
Anyway it's not mutually exclusive; you can distribute an APK as well as use the official alpha/beta rollouts. Having heard demand for Kindle usage, we sometimes post APKs in our beta community as an attachment to posts announcing a new build. So sideloaders can directly install the APK while Play users get an alert about what's incoming to their device.
