I've always struggled with this, as both a babysitter and as a nanny. (I worry less about it as a babysitter since I'm with the kids for short chunks of time, but as a nanny when I'm with the kids for extended periods of time, it is a concern.)
I read an interesting article about how kids nowadays just don't know how to play by themselves. They're so used to being in front of the TV, or with a parent or babysitter or nanny--in the name of watching them to keep them safe--that they don't know how to use their own imaginations by themselves or with other siblings.
My girls A. & E. with my former family didn't know how to play at all when I started working full-time with them. They were so used to being in front of the TV that they literally didn't know what to do on their own. I worked for months helping them to learn different activities and things to do, helping to develop their imaginations, and slowly worked up to having them play off in the living room while I was making dinner in the kitchen. They learned to entertain themselves.
When my sister and I were younger, we'd spend hours off playing school, or doctor, or "adoption" together, in and outdoors. Our parents played with us a great deal, but we played alone a lot, too.
Kids with nannies don't really play alone, though, because it's lazy babysitting/nannying for the babysitter/nanny to sit off in the next room, letting the kids play. Does that make sense? In other words, why would a parent hire someone to just sit elsewhere, not be with the kids?
I've talked with fellow nannies about this. We want to encourage self-play in our kids while at the same time staying in our bosses' good graces. In my past experience, the kids I've nannied/babysat for turn to me to entertain them constantly--because it's my job. But kids who are constantly being entertained by someone or something else don't develop self-play/entertainment skills and, therefore, are much more demanding on the whole.
I'm not saying that as a nanny, I'd want to leave my kids to self-play all day. Not at all! Playing with a nanny is a great interaction and wonderful for social skills. I love playing zoo keeper, baby wrangler (when the big kids want to be babies), etc. But I also think that it's important that, for a certain chunk of time each day, the kids play by themselves, learning to keep themselves occupied and discovering their own imaginations.
A stay-at-home-mom or dad has various tasks to complete during the day, like cooking, cleaning, or working from home. As nannies, our sole purpose is to dedicate ourselves to the kids. And it's great fun for kids to have dedication like that! But I do wonder, in the big picture, if it is a problem?
P.S. I have *no* idea if this post makes sense or not! But it does in my head :)