I haven’t used a tow bar in 30 years, and I don’t remember the OD of the pins, but they are not flimsy. There is very little load on those pins. They might even be off the shelf 5/8” hitch pins.
For perspective, a trailer hitch drawbar uses one 5/8” hitch pin, no matter the size of the hitch, from class 1 all the way to class V, which is greater than 10,000lbs.
I think they are usually 1/2" bolts. And you're right, there is very little load on them, the U-shaped pieces take almost all of that.
I never put a safety chain to the vehicle, but I do believe that is the law in some states. I did have crossed chains from the bar to the tow vehicle's hitch though.
I still have my tow bar. I am not selling it or giving it away, but I do hope I never need it.