Because of their age children have no chance to earn thier own money in most countries. I'm not saying children should work all day long, no, they should rather study, but it they have a chance to earn a little, working not more than 1 hour per day, that's great IMO. And Bitcoin gives them that chance.
A lot of children are earning but most likely in illegal ways specially in 3rd world countries. They are being exploited everywhere like peddle drugs and sexploitation. My point is, not every children can be given equal chance to earn with bitcoin. Those children or kids at a young age which can potential earn bitcoin is very lucky specially in USA or UK unlike their counterparts in other side of the globe, which have to do hard labor and sometimes exploited to earn money just to survived.
If you answer the question posed, then you can already say with certainty that there are plenty of opportunities to earn money for children on the Internet. But only you need to answer the question of what you need to do to earn money. If you participate in the signatures of companies, then this is one and quite an easy task, and if more complex conditions, then what age will it take to perform work qualitatively?