It's open in the sense that anyone can use it. Without restriction. And there's no way to be banned from it. Since anyone can just drop off an anonymous letter in the post. You don't have to enter a service agreement. Just dump you satchel of letters with stamps on them, in the nearest mail box.

It's not just practically open. It's legally open; at least here in Canada, the federal postal service has a legal obligation, arising from the constitutional right to free speech, to carry any mail that has legal content, regardless of how Canada Post or its employees might feel about it. They're obligated to take those commercial service agreements regardless of content. (This has been a point of contention sometimes with graphic anti-abortion flyers delivered as ad-mail.)

The main means to deal with someone abusing the postal system is the criminal law and court orders.