I've never seen much drama in low-speed tire failures on cars, either.
Looking at the tire sizes you suggest:
175mm = 6.88976378 inches tread width. (6.9" for ease)
The overall circumference of a 175/70R13 tires is 71.12 inches, figuring total area which will make road contact during the rotation of the tire:
71.12*6.9 = ~490.75 square inches.
The trailer tire has 4.8 inches of tread width, and close to 20" diameter.
Pi*20 = 62.8318531
62.8 * 4.8 = 301.44 square inches.
By your admission, a trailer tire at nominal inflation pressure can handle 785#, and a 175/70R13 tire can handle 1036#
Dividing out:
785 / 301.4 = 2.60451228, or 2.6# of capacity per sq. in. of tread face.
1036 / 490 = 2.11428571, or 2.1# per square inch...
Hm. seems like the trailer tire is actually
stronger? We can't really assume that, because I estimated the diameter of a trailer tire. It's been awhile since I've measured one.
As far as handling, braking, etc... yeah, those things actually
are designed into trailer tires... trailers have brakes, my friend. They also have to maintain a course in a straight line behind the towing vehicle, which means that they have grip while cornering. It may not be the same handling characteristics as a car tire might have, since they're not designed to
be car tires, but for a very small city vehicle, I still don't see a safety issue.