The proof obligation is the other way around. You need to show that constant surveillance actually makes a difference, on a population level. Otherwise your claim is the empty one.
Unfortunately, I only had time to do a quick search, but it shows that mortality has dropped significantly in the last 20 years. I imagine it was only higher 40-60 years ago. This doesn't prove that more surveillance brings mortality down, but it shows that the "we survived just fine" argument is shaky at best.
I think parental supervision correlates with the survivability of offspring in general, not only in the human species. Also, the more present and engaged parents are, the better the children are. This is supported by research on children raised by single parents, parents working multiple jobs and shifts.