I hate to disagree... I mean hey it's nice that you try to come up with new ideas for the game but if the chat sections were switched like that, there would be a waterfall of people talking, and you wouldn't even have the time to read the relevant messages (e.g.messages you're mentioned in, your friend's messages, or messages from people who are in need for help!)
Don't you see that would be pretty stupid? Also there's a good reason behind party chat and group chat: It's so people can have private conversations with each other. It would (as Valhayes and Azura mentioned) be absurd, complicated, confusing AND frustrating at the same time, if you could only do private talk with one person at a time.
If you didn't know this, General chat was permanently removed in public maps due to the lack of faith in people. There were a waterfall of spams, CAPSLOCK lines, and unnecessary nonsense messages. It was a real problem because General flooded the chat (meaning it was difficult to read the necessary messages in for example Whisper, Local, Group, ect. ...)
I really apologize for my mean and harsh tone here, but I just don't think you've put real efforts and thoughts to this idea. :l