Letting your kids watch cartoons is NOT supposed to be educational. In fact, screen time and being "plugged in" has a really bad rap and parents are encouraged to "unplug" their kids and get them reading or building or playing outside.
And kids should read and build and go play outside.
But I also let my kids have more screen time than others recommend, and I'm not too worried about it. They are not lacking in time to do all the other good things, and they are not passive consumers - they are engaged with what they are watching.
In fact, last week I got them a disc of Super Hero Squad from netflix, which they watched happily about three times through. This led to a conversation about "The Marvel Universe", which led to me having to do some online research (thank you Wikipedia!) because I knew nothing about comic book heroes or the whole "DC versus Marvel" conversation.
And that led to a trip to our local comic book shop, and the purchase of a Super Hero Squad comic book. Carbon has been struggling his way through reading it independently - and that's the first time he's tried this hard to read something all by himself.
Reading a comic book has led to wanting to create a comic book, and lots of drawing time for both kids. And that also led to some great conversations about what the law is for copying a character - we had to once again consult the internet for some copyright law information (thank you, Wikipedia!).
Carbon decided he wanted to buy a toy related to this whole thing, so we went to the store and found out how much that would cost. Then he's been saving up for that toy, and doing a bunch of extra work to earn money. I had flower bulbs that needed to be planted, so I offered that as a paid task. He had to be shown how to properly plant them, and then he spent hours outside planting flowers so he could earn the money to (he planted 100 flower bulbs). So he ended up spending time outside too!
(Hypatia's comic heroes)
Overall, not a bad cascade of results from letting my kids watch a cartoon! I don't think it's the time spent being "plugged in" or "unplugged" - I think it's how plugged in the adult is to the child - how much you are noticing their interests and then giving them the resources they need (including their time and your interest and your time) so they can engage with their interests.