I think you're stretching the idea of compelled speech to the point where it loses its essential meaning. Compelled speech is when someone forces you to say something, not when you are prevented from disallowing someone to say something under their own name on your website/property.

When I comment on HN I do not comment as HN itself.

What you're talking about seems like an application of the idea of private property rights (i.e. kicking someone out of your house/office for saying something you don't like).