Identify devices, not people.
Distinguishing between child-locked and unlocked devices is something any website should be able to do easily. Adult-only should be a config setting.
Vendors shouldn't sell unlocked devices to kids.
Then it's up to parents take sure their kids only have locked devices. (Or not, if they're okay with it.)
What for? I use family link for my kids devices. It works good enough. Everything else seems way too intrusive.
Apple is horrible in this regard. Their solutions never really work.
A joint venture for an (optional) cross-platform family app would be more than enough. This, plus a (voluntary) content rating that's offered via an API (could even be simple meta data on a webpage). Done.
> Vendors shouldn't sell unlocked devices to kids.
This part is neither necessary nor sufficient.
Put aside the Orwellian premise of "devices are locked by default". People keep making the analogy to things like cigarettes, but if a kid wants a steady supply of cigarettes then they need a steady supplier. If they want an "unlocked device" they just need money and Craigslist, once. It doesn't matter what you make Walmart do and it correspondingly doesn't make any sense to involve them.
If your kids have enough unsupervised money to buy electronics then you're either fine with them being unsupervised or you already have bigger problems than a used laptop.