I think that independent play is good. I think that children should be able to find constructive ways to use their time and that their parents should not be their sole source of entertainment. Yes, you should play with your kids. And you should read to your kids. And you should teach your kids. But, I do not believe that mothers (or fathers for that matter) should spend all of their time micromanaging their children. There are other things that need to be done and showing your children how to balance responsibilities is just as important as keeping them "busy."
With that said, it's obvious that I give my children a fair amount of time to play with each other. My office is directly off of their playroom, so I can work and be within earshot at all times. Yesterday, while I was replying to some emails, I overheard Doodle and Dilly playing one of their games.
Doodle: "You need to take it easy. You have a baby in your belly."
Dilly: "Baby belly."
Doodle: "Yes, there's a baby in your belly. Let me check it."
Dilly: "Baby Pablo."
I didn't interrupt. I just kind of laughed and kept working. A few minutes later when I finally turned around I got the best surprise of all. Dilly actually looked pregnant. The two of them had unzipped Dilly's sweatshirt, shoved a stuffed animal in (Pablo from The Backyardigans) and re-zipped. It was classic. And exactly what I should have expected for letting them play alone ...