We even raced on the interstate highway interchanges before they were open to regular traffic. We regularly ran at the local fairgrounds, school and supermarket parking lots, etc. Public ground was the same deal - usually avaiable throughout the weekend.
In the late 50s, you were pretty much free to drive or race in anyone's parking lot on Sunday afternoons (very few stores - at least in the midwest - were open on Sunday back then). That may have been the case for some, but for the average karter back in the day (and there were thousands of them), it was a matter of noplace to drive them - due to insurance liability after a handful of tragic accidents on municipal and private land. "I am sure the reason it died was the expense that it evolved into." When the cops came we'd tell them it was Federal property and they were out of their City jurisdiction, then they'd make a radio call and get in their cars and leave.! We usta flat tow them a mile and a half behind a bicycle to an abandoned piece of Navy property just south of the Long Beach Airport and run them their. They would wind tight but the bottom end torque sucked so if you slowed down it would die easy. I remember base Go-Kart go-karts typically ran 2 stroke McCullough chainsaw engines direct with no clutch. If it's for dirt track use, use a solid rear axle with both wheels driven. If you want to ride it mostly on pavement, and not dirt, make it a one wheel drive.
The frame is going to be a couple of rails about 16" apart with the front axle doubling as the X member and the rear overhang adequate for the engine. If I was making one for ME I'd cut the legs off an old chair, get some chalk and a measuring tape and an assistant and sit in the chair on the garage floor and measure up where I wanted the pedals and steering wheel from there. "Some older guy got too big for his 1/4 midget and took the body off so he could sit on top of it instead of in it and still ride it.!" When Go-Karts first hit the scene, I was a smart 5th grader and I took one look at them and said to myself. I know this doesn't answer your Q much, but