ah, the visitor messages ! these were the source of much confusion when they were first implemented, and much discussion about how to properly use them : reply to them directly on your own page, or on the other person's page ? the first option makes continued conversation dependent on the other participant remembering to go back there to check for a reply from time to time, but the second option seemed disjointed to some people... until they discovered the "view conversation" button.
your idea of linking from the user cp directly to the conversation is interesting, but like you said there are frequently 3-person conversations going on...
for your question, myself, i read the comments on my own page (so i can see if anybody else is participating there) then i usually click "view conversation" to reply so i can see the comment i am replying to and the previous conversation, and then i go to the other person's page, to see if anybody else is participating *there*.
it's a whole process.
i admit i like it though.