So far, very few parents have actually tried it. I saw one pair of toddlers in the session I popped into briefly this afternoon, but I haven't used it for my own toddler, and it's mostly been childless folks talking with each other.
My son's music teacher from daycare has also started offering entertainment via videochat (along with his two kids), and my son's enjoyed it, but he's still fully supervised and it hasn't taken any load off my wife and me.
As a parent, I see two big problems with it:
1.) Scheduling. Logistically, being a parent and working from home is already really challenging, and it's pretty unlikely that the times your single friends or educators are free lines up with the needs of your kid or work schedule. (Inverting the scheduling so that parents propose the time may help with that, but parents are generally too busy to propose times and check for a response these days.)
2.) Trust. Pre-schoolers (the age range with the biggest time crunch) cannot generally be trusted to be alone with a computer. I've tried using PBSKids as a babysitter, and my kid nearly broke my touch screen, tossed the laptop off the couch twice, almost deleted my code (thank god for undo and version control), and asks for the channel to be changed every 10-15 minutes because that's his attention span.
Being completely raised by the book as Nell is wasn't what the book was intended for either by it's creator, Hackworth, or the patron, Finkle-McGraw. It was instead intended as a supplement for the failings of traditional education.
For small kids all of the online options are only supplements to the interactions and learning that happens offline. The digital interfaces are still to clunky for them to learn much from anything but meatspace interactions with people and their environment.
That being said I appreciate Siri answering why questions 100+ times a day.
As a parent it would need to be FOSS though.
Then, a lot of performing arts folks I know are trying to find work, and one of the suggestions is remote nanny'ing (aka, entertaining your kids over video),
I think there's an opportunity to self-organize people to address these things. Out among all of us us, there's enough expertise, desire and shared need.