Right on Schatze! I agree with everything you've said.
Gotta consider both sides of the coin!
The other thing I like about PMs is that it's instant.
Boop & it's done. It's quicker than an email. There are lots of times when I have PM'd something that I wouldn't take the time to do in an email. It's a convenience.
I recently PM'd a moderator asking them to pull a thread I had started because another poster PM'd me & told me of a situation regarding a news topic I reported on.
While the other poster did not ask me to pull it, I decided that on my own, but it was sure convenient to handle it in a few short keystrokes. I don't stay signed in to my email address, but if I am visiting a forum, then the PM feature is right there.
And you're right, I had neither ones email address.