peter 337, Don't get me started on towbars!
My aeroplane had a towbar incident just like you describe (before I owned it). I am absolutely firm about this; You fit the towbar, move the aeroplane then remove the towbar and leave it on the ground beside the nosewheel. I am up to here with telling people not to leave the towbar on the noseleg
Instructors have a responsibility to demonstrate this sort of thing when moving aeroplane on the ground - it's all good airmanship!
Happy landings
3 point