surveillance [1]
n. Close observation of person or group, especially one under suspicion.
n. The act of observing or the condition of being observed.
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This is CERTAINLY your responsibility toward your children. (The lack of it is known as "neglect".)
Personally, I do not let my 6 year old go to the small neighborhood park by himself. But if he has a remote monitoring device, I do.
As he gets older, there will be other cases where he will be allowed to do things only under some type of supervision.
Obviously it varies by age and maturity, where age 0 requires earshot proximity, and age 17.5 requires comparatively minimal attention to diet, education, and recreation.
"No surveillance full stop" is simply wrong.
"No electronic surveillance" is I think unwise and ignores opportunities for safe, constructive experiences.
"No secret surveillance" is I think a fair statement.