I think you may be underestimating how easy some old cars were to steal. Alarms aren't perfect, but they're noisy and paranoia inducing. In some cases starting an old car could have been a matter of opening the door with a clothes hanger (these things weren't sealed too tight), pulling out the key thing, moving it aside and using a coin or something to turn the ignition.

They were also worth something. It just isn't as easy in most places to flog a stolen car. At least not factoring for inflation or something, I guess. The economics of crime shift just like everything else.

Sometimes stuff police or politicians or somesuch do helps too. Anything is possible.