Inherit permissions from root page possible?

I’m trying to require users to login to view any page. I’ve started by enabling “Use parent access rules” in the Login plugin.
I set up a testpage and a subpage as a child of the testpage and set the testpage to require site.login. Both the testpage and the childpage now show a login form.

I’ve tried to extend this to the whole site, by setting an access rule for “site.login” on the root page, but it seemingly gets ignored.

Is the root page treated specially by the login system? Is there a simple way to achieve my goal? I’ve seen the “private site” plugin, but being beta and not having any changes in the repo for 4 years does not fill me with confidence…