No, I don't think it'd be consistent with how we defer to parents for other things that require consent. For instance, parents or guardians are always the go-to for granting consent for their children in anything from vaccines, to public school attendance, to sports participation, travel, and everything else.
But, still, I'm uncomfortable sharing photos and videos of my children online. I know my wife does on Instagram, and it's not ... to make my daughter "Instagram famous" or something, but it's because our daughter is such an important part of our lives, and my wife regularly shares cute photos of her, videos of her doing silly things, her first steps, etc., and the people who care about us like watching those videos or seeing those photos.
I upload thousands of photos/videos of my daughter to Google Photos, and share those with my parents, in-laws, close relatives and family friends. They love seeing the photos and videos. I think making this illegal might be too strict.
Clearly there's something uncomfortable about parents who monetize their children without their consent and try to turn them into social media stars. There's something we don't like about as a culture, for the same reason that -- when I was younger -- I hated the child beauty pageants and other people might hate child participation in sports, science fairs, and other perfomative acts that parents push their children into. Unfortunately, I don't think the framework of making those things illegal is the right thing to do, but I'm definitely uncomfortable with many of them.
When it comes to something like child labor or "unpaid volunteerism," I think that's a bit of a stretch. When I was a kid I was an unpaid "volunteer" (Actually it was always involuntary...) raking leaves every weekend in the fall, mowing the lawn every Saturday in the summer, shoveling snow in the winter, and doing the dishwasher or helping out around the house. I wasn't paid for this. When my kids are of age, I'm not going to pay them to do their chores. But, I also lived under my parents' roof for ~18 years, they bought my clothes, got me gifts for christmas and birthdays, paid for and cooked meals; it's part of being in a family. I'll likely raise my kids the same way.
I'm still uncomfortable uploading videos of my kids to public spaces, I don't think I ever really will, but I don't think that a law banning it is the right approach... Rather merely address each situation individually. Instances that are objectively harmful to the children should be investigated using the tools we have -- child and family services, for instance.