Whatever Happened to Teen Babysitters?
theatlantic.com
theatlantic.com
Coupled with the fact that many people leave their families to start afresh in a new city to make a career and their own family, and there just aren't many teens around you know of that you can even ask for babysitting.
Then consider the teen side. I would probably rather work a part time job than to try and get a network of clients with young kids together that would bring me enough regular work to beat out that. A network that is smaller and more diffuse today than in our parents generation for the same reasons that the teen network is smaller.
My perception is that this has always been a class thing and the answer to a lot of the "whatever happened to X" questions is that the journalist grew up in a lower class bracket than where they currently find themselves.