It was a very different world 50 years ago, I was seven and no-one said much about sexual abuse then.
Children were left with people not known and still are, it can't be avoided - teachers, doctors, nurses, youth workers for example. Fifty years ago all of those had far more authority than they do now & there were not so many background checks. (The vast majority were fine.)
In any case, most abuse is carried out by friends or family.
When I was a child people seemed to like Jimmy Saville, eccentric, fun and all that which is how he got away with it for so long. What particularly horrified me about the cases that came to light was the thought of him molesting innocent children in hospital who maybe could not move or speak. Not just children, it's makes my stomach churn. He was a revolting piece of work.
I don't know about Ted Heath. A few years ago someone I know well told me a few things about him, that they had been told, but I recall saying at the time it was only hearsay. I don't see how anything can be proven now but it can help victims of historical abuse to talk or write about it, it breaks the hold the abuser has had on them. They have to be careful who they are talking to though because any victim remains vulnerable. They need to be sure that they protect themselves.