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I think our author is creating a problem where none exists.
If you want kids to learn programming on their own, here are the three rules:
It's got to be fun
It's got to be free
It's got to be easy
Fortunately, there is a line-oriented programming language that already exists on every home computer on the planet, and it meets all three criteria. It's called Javascript. It runs in your browser. And it teaches everything you would learn from BASIC.
What, indeed, do you learn from BASIC? Well, you learn about variables, subroutines/functions/methods, and about "if", "for", "while", and "print" commands, and about basic I/O. Javascript, like pretty much all programming languages, has all that.
Plus it meets the first criteria: It lets you do fun stuff. You can make things happen on web pages, and post them for your friends to see.
I learned to write code in the '70s in grade school, and my first program was a variation on the old StarTrek game. I spent hours obsessively adding new features to a program that you played on a clackety-clack teletype. No video back then; just paper and ink for output. I would not have done it unless it were just plain fun.
So don't lament the loss of BASIC; it wouldn't work anyway, because it's just not fun anymore. And don't think for a moment that it is in any way superior to Javascript or a zillion other easily-obtained languages. The concepts are all the same. I'm not worried about the kids.