Actually I think this can be easily fixed by not allowing to do "New Game" on an existing profile, making it one profile = one party.
Since you can create multiple profiles, I don't really see the point in starting several games using the same one.
I don't know about that. Profiles are also good if you have family members playing the game (at different times) on the same computer. "Dad's Game, Mom's Game, Timmy's Game" etc. Each making a new profile for each new game would get pretty cluttered quickly.
I just wish co-op saves were stored to each player's machine. Manually transferring them to each other is a bit of a pain.