These kids can't access any services because they don't legally exist in government systems. No birth certificate means no school enrollment, no healthcare, no social grants.
You think a 15-year-old footballer who can't play in tournaments because he has no birth certificate is going to be helped by Bitcoin?
What school is letting them enroll because they have a hardware wallet?
This is a civil administration problem that needs government solutions: streamlined processes, digital systems, reduced fees, and political will.
However I don't see the binary extremes you see.
The undocumented people can pool together and start their own schools. They can start their own soccer league. They can hire a pooled doctor. They can put some amount of stored value into a crypto account, which might be better in some cases than hiding gold in a hole or something, because they aren't going to be able to access banking.
And yes, that situation sucks, and it's wrong, and it encourages apartheid-light, and is not an acceptable solution. But in the meanwhile, it would be better for them than nothing and it is something they might have the agency to do.
So there's already a lack of a stable, functioning government, and the solution you're touting isn't currently a reality, why? In the US when there's little friction in a marketplace people in some communities resort to using Tide laundry detergent as a medium of exchange. There's nothing stopping them from using bitcoin or cryptocurrencies currently, but navigating a market place, finding qualified teachers, finding motivation to use what little resources you have to use a novel medium to pay for teachers in a place with no opportunity, etc., doesn't seem too easy. One tool alone doesn't usually solve any problems.
Back in 2013, I loved the idea of Bitcoin. Then I actually tried using it. Such a pain. I switched to Coinbase until I gave up entirely on crypto around 2017 and became highly skeptical it was going to change the world as promised. I would love to hear that the world of self-custodied Bitcoin has become less onerous.
I completely agree. The world of developmental economics has had so many great "One tool to fix everything!" ideas, but at the end of the day, they generally don't add up to much without a functioning government that's focused on serving its citizens.