But we already have that and it doesn't work. Sites don't bother to classify themselves. Whitelists are spotty and out of date. Almost nothing interoperates properly. My expectation given the scenario you describe is that business continues as usual with the vast majority of the internet thus being inaccessible when in "child" mode. As a result no one uses child mode and the vicious cycle perpetuates.
A solution would be browsers refusing to load any site that didn't provide such metadata, not just in child mode but in any mode. I suppose either Apple or Google would likely be capable of unilaterally imposing such a requirement as things currently stand. However I also think that's unlikely to happen on its own for various reasons. Thus legally mandating certain basic content classification categories in addition to an extensible standard protocol for communicating such metadata would (I expect) end the cycle. And rather than the government going after individuals the legislation could be structured to place the onus on mainstream browsers, OSes, and other client software to enforce compliance on their behalf.
We are seeking a solution to a social problem, not just a technical problem. If it fails to achieve most of the social goals, it won't be used and you get something worse. Welcome to the real world.
The standard OP is describing doesn't exist. So whether it "fails to achieve most of the social goals" is yet to be determined. Blocking unrated content seems like a pretty desirable feature to me. Why wouldn't that be one of the "social goals"?
You can turn on filtering and subscribe to a whitelist today. People don't seem to be satisfied with that solution. Why not? The answer to that question is what needs to be solved.
There's no web standard for labeling content, so "subscribe to a whitelist" today means crappy page or network-level content blocks implemented by a third party tool that has no understanding of the actual content on the page or application. That's not at all what's being proposed in this thread.
With a universal labeling standard the UX would be much better, and there'd be a much greater incentive for website owners to participate (they'd be implementing a universal standard, not adding support for one particular parental control tool).
But the expected result here is that parental controls continue not to work very well, parents continue not to use them (at least competently), and people continue complaining that something needs to be done. So I propose that we do something about that rather than sit around continuing to roll the dice on the next half assed turnkey authoritarian solution than an inept legislator fields courtesy of a lobbyist working for a megacorporation whose interests tread well into the realm of the blatantly evil.
A solution would be browsers refusing to load any site that didn't provide such metadata, not just in child mode but in any mode. I suppose either Apple or Google would likely be capable of unilaterally imposing such a requirement as things currently stand. However I also think that's unlikely to happen on its own for various reasons. Thus legally mandating certain basic content classification categories in addition to an extensible standard protocol for communicating such metadata would (I expect) end the cycle. And rather than the government going after individuals the legislation could be structured to place the onus on mainstream browsers, OSes, and other client software to enforce compliance on their behalf.