I use UltraVNC because you can reverse the connection order, allowing a server to connect to a client and avoiding firewall hassles if you're troubleshooting a remote computer for somebody who doesn't understand such things.
Do they have one-click connecting? I'm not in love with UltraVNC, but it's by far the most user friendly software I've found because you can eliminate 100% of configuration for one of the users. You compile an executable using their web tool, then you have the person just run the program and they're done.
If better software allows the same functionality, I'd drop UltraVNC in a heartbeat.
Not that I know of, the user to be controlled would need to right click the system tray icon and enter the listening viewers IP in the add listening viewer option.
I can see why what you describe above would be useful though.