> Before app verification any app store could install any app without having the user jump through crazy hoops

After app verification, exactly the same. Nothing changes about what app stores can do.

> App verification does not "allow" anything

It allows installing apps outside a system app store without the user having to enable installing from the app that triggered the install. Prior to app verification , the user had to click through a dialog to go to settings to allow installation from the app that triggered the install.

> You cannot view app verification's existence without considering the broader environment it was created for.

Exactly right. The broader environment was that Google was forced to allow installation of apps outside of system app stores without the user having to tap through a warning dialog. This is the solution to that problem.

> After app verification, exactly the same.

No, because to install unverified apps the user has to 1) enable developer mode, 2) confirm you aren't being guided, 3) reboot the device, 4) wait 24 hours, 5) enable unverified app installation. You also have to confirm that you are really-really sure with every install. Oh, and that step 5? Google explicitly recommends turning it on for 7 days only.

> It allows installing apps outside a system app store without the user having to enable installing from the app that triggered the install.

... which was already possible, so it is not enabled by app verification.

> You are confusing app verification with a change in how to install unverified apps.

It is two parts of the same thing. App verification exists only to make installing unverified apps difficult. App verification has no reason to exist if installing unverified apps is not restricted.