Depends. The refusal bit is a bit questionable. DS, who is now 12, refuses to do stuff. But that comes at a price to him. No PS4, or something he's looking forward to doing. Because he has to learn that there are things we HAVE to do and things we WANT to do. I don't particularly enjoy hoovering, but it'd be a pig sty if I or DH didn't do it.
But there are a lot of things that can be used. DS is enjoying the new bitesize things on the BBC. We watch the bitesize lessons on TV at lunch time on IPlayer - he thinks they're quite funny but he's joining in with the tests etc so is taking it in. Then he does the things on line because they're fun.
We're going to watch Blue Planet when I get off of here. Not on the curriculum but it'll include geography, conservation, animals so he'll be picking something up. He also likes the NASA site as it's got games and science stuff which he loves.
It's all about finding things that interest them. Even Horrible Histories teaches kids about different civilisations or times and if it provokes an interest you can build on it with documentaries, books, on line stuff.
So, no, learning doesn't have to be formal. But, yes, if there's work set it should be done just to instil the idea, gently, that life isn't all about getting your own way and there has to be a balance.