> if Reddit bans you, you aren't entitled to use the site

I would say that you are not allowed to use their site as a logged in user (i.e. upvoting, downvoting, commenting, making posts).

It does not seem logical to me that Reddit could "ban" anyone from using their public frontends as anonymous users.

They could only do something like that, in my opinion, if access to all their content was gated behind a login.