Just my 2 cents here. I typically use the tow hook to pull the car in the trailer and depending on which trailer I'm using, I winch it back out (if the side door is not lined up with the car door) or drive it out. This eliminates climbing in and out of windows and saves the clutch.
The only concern I would have with leaving the hook on the car all the time is the potential for it to loosen up from vibration eventually causing it to fall off (not very likely) or that somebody might decide it would be a nice souvenir (if you left your car parked unattended somewhere). Both of those are highly unlikely scenarios, but depending on your situation, they may be a concern.
One of the great members of this forum (thanks Kirk!) went to the trouble to buy me my very own tow hook so I don't have to use the customer's. Just another nice touch to keep these cars pristine.