Years ago when I was an apprentice AME, it was drilled into me that all doors must be closed when towing or moving a pressurised aircraft.
Reason being was due to the airframe structural integrity potentially being compromised if a door was left open. I actually believe it was a standard practice throughout the industry back then. I wouldn’t be surprised if the manufacturer’s maintenance procedures mandate the closure of all doors and hatches when the aircraft is under tow.