Yes, and if I have a public Twitter account it’s perfectly possible for someone to flood me with spam messages. That doesn’t mean we should do nothing to prevent it. As I said elsewhere, we should strive to make it possible for people to exist in public digital spaces without worrying about bad actors.
Someone can manually spam you, and I don't think that should be allowed. That is a separate topic and discussion. Unless you are arguing that your employer should not be allowed to check your LinkedIn status.
I’m just using it as an example of a case in which a public profile doesn’t automatically mean anything goes. I had hoped to generate discussion about how to throw out some of the bathwater without throwing out the baby too, but I guess no one is really interested.