I had a chopper as a kid, 26" Schwinn with a raked neck, straight 4 ft. fork, 20 inch wheels and a 48 inch sissy bar. A friend's Dad did the frame and fork, he got it aligned perfectly and put ballast in the fork legs. You could lean back on the sissy bar and let go of the handle bars and it would go straight as a string for blocks. Turning corners with no hands was a bit of a challenge as it wanted to go in a straight line no matter what but as long as it wasn't too sharp and the pavement was clean it could be done.

IIRC the first production bike I couldn't successfully ride hands free was my Miyata 510 back around 1982. Even hands on it was a bit "twitchy", I never really warmed up to that one. It was a good looking bike but I never really enjoyed riding it. I bought it used at the LBS, a guy bought it and only kept it a couple months then traded it in on a different bike. He didn't like the way it rode either. I had 3 other road bikes about 10-15 years ago, I could only ride one of those hands free and then only a short distance.