If you're willing not only to download sideload apps but also to modify your device so you can have root access, then it works. So not really different from Apple.
Moreover, the ad blocking features you get without root are a strict superset of the features that are possible at all on iOS.
You can do it without "circumventing the system software." Unlocking the system partition is a supported operation. Then just install a program that lets you run other programs as uid 0. This is not possible for normal apps to do because running as uid 0 means you are no longer subject to the permissions system.
Also, it's irrelevant because the whole point is that Google can't block the user from running whatever apps they like by blocking the app from the Play Store. Requiring root access is orthogonal to Play Store availability.
Users running their own apps as uid 0 goes directly against the security model. Nothing stops them from changing or completely discarding the security model on their own devices, but once again, that is completely orthogonal to blocking apps on the Play Store.