No I certainly do not leave the water running!
I have an electric toothbrush that brushes for 2 minutes before "beeping".
I would not let water run that far as there are huge water restrictions in Perth and we have had nowhere near enough water for many years.
Dams are only one quarter full or some such and we can only water twice a week, so I think it is irresponsible to leave water running for 2 minutes for no reason.
I do not even leave it on while washing my hands which is far shorter -i am not generally so environmentally conscious however with water and our lack of it in WA, i am.