Yeah, the “ordinary” bikes are pretty scary. I had a chance to try to ride a 48" bike and I comletely failed. The biggest danger, as I understand it, is the “header,” i.e. being thrown over the handlebar and onto your head. Ordinary bikes have very skewed (front heavy) weight distribution so it doesn’t take much to tip it forward.
By the way I question casdave’s claim that the invention of the chain and sprocket made the safety bike possible. IMO the invention of the pneumatic tire was a more significant factor. With solid rubber tires you need big wheels to reduce rolling resistance and to make the ride smoother.