Tires are the only thing between you and the asphalt. I dont believe I would chance it unless the truck is going to be used for an occassionl parade or show and even then I would be very careful driving it.
I agree that rubber of today is nothing like rubber from the 60s/70s but the important part is the structure and I will bet that technology of today far offsets any loss you may have in strength of todays rubber.
The tires of yesteryear were built to drive at far lower speeds and with lots less chances of accidents and in my opionon are not suitable for nowadays conditions.
Hobert
