Hi,
I think the only relevant argument is that it is a waste of power. If you have power management turned on then this should be minimal.
If a hacker can get you then they can get you while you are using it, they dont have to wait until you go away. As long as you have a natted router and antivirus then you should be completely safe.
As far as itunes, emule et al sucking up your bandwidth you can monitor this; also it is possible to set emule etc to limit them to a certain amount of upload bandwidth.
Anyway, my teenage daughter is the same, it annoys the hell out of me but I have leant to live with it
Paul