My suggestion would be to not show the welcome messages in the sender’s PMs until there is a reply. (Filter it out from the message lists and counts until posts > 1.)
Is there any common scenario you’d want to see it otherwise? I guess it helps keep tabs on the latest users to join in case you want to reach out to someone you might already know, but that seems rare.
I changed my default sender to @system a while back because my inbox was getting crazy (I don’t know how you manage @codinghorror!) but am realizing that I’ve probably missed out on users replying to the welcome messages, which is unfortunate.