It was also a safer world.
Safer in what way exactly?
[1] Crime rates have been falling steadily for decades even though
[2] there are many more crimes you can be charged with today than there were in the past. If you're talking specifically about white collar crime then I would strongly agree with you, but in the case of blue collar crime your contention isn't supported by the majority of statistics I've seen. Speaking of statistics, while you're busy watching and waiting for strangers in a public restroom to "try anything"
[3] the far more likely predator profiles are already known to you and are welcome in your own home. But please don't let messy things like objective statistical analysis stop you from spending as much time and effort as possible worrying about some of the least likely threats to your family.