It's not true that everyone would be happy. Banning an otherwise fine and on-topic site leads to angry complaints that we've banned it for unfair reasons. Nobody thinks, "oh, I guess they banned it because the site owner asked them to".
If they don't want people visiting their website maybe they shouldn't put it on the internet.
Aside from the actual situation, this pattern of words seems reminiscent of victim blaming.
They could add a login form if they don't want their website to be publicly accessible.