When did letting our kids out of sight become so scary?

I don't remember when I started playing outside alone. I don't remember either of my parents saying "No" to a request to head outdoors for the day, or watching from the window constantly. I do remember having a curfew of street lights, or the dreaded yell from mom.  I do remember playing in the yard, at the park, or at neighbor's. Nothing terrible ever happened to any of us. We went home dirty, maybe a little bruised up, and ready for bed and a new day to play. 

Every day I fight the worry of what could happen to my kids. Monkey could fall off the edge of the couch she's always bouncing on. Fitz could be approached by a stranger outside and be her usual overly friendly self. Someone could get stung by one of the wasps that seem to make our deck their home every summer. 

When did I become that mom? I don't like it. 

When did letting our kids out of sight become so scary? 

Fitz has begun asking to play outside by herself more and more frequently. She loves riding her bike, she thrives on dramatic play, and could swing herself for hours. Everything kids should be outside doing. "Go outside and play" should be on the tip of all parents' tongues when the weather is nice and the kids are well. And yet, I hesitate every time. 

At what age did your kids start playing outside alone? Does it make you nervous, too?