I don’t teach my kids to swim, yet I let them go to the pool by themselves, because anyhow they go out in the rain.
Keddushin 29a:
????? ??? ??”? ??? ???? ???? ????? ??????? ?????? ???? ??????? ??? ?????? ?????? ??”? ?? ?????? ???? ??? ????? ???? ?? ????? ???? ?? ??? ?????? ????? ??????
Not surprising, since Frum people B’shitah ignore Chazal regarding ??????, they also ignore Chazal regarding ?????? ????
;-p
Seriously, I’m not suggesting taking your children to Times Square. It is a matter of degree (as you seem to admit), and the question is where to draw the line. As explained earlier, it has to be dependent on the child him/her-self. The child can just as easily walk/bike into the library on their own if they so desire.