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Lets face it, BASIC is dead. And it should be, because it is too limited to do anything useful in todays computing environments. I see your points about how BASIC was a very accisable language for a kid to tinker with and understand how a computer works. I see today's equivalent is writing a web page. My 13 year old cousing wrote her own web page, first in just HTML, then added some client side script (java script) and then added server side script (Visual Basic Script). This was much more interesting and useful to her than making a dot move across a screen, as she could share it with he friends and get instand feedback from her friends. Windows comes with a Visual Basic Script interpreter, anybody can write in VBS and save it to a .vbs file and execute it.
When you make the comparison to a docutor needing to study chemistry, etc, this doesn't apply to the rest of your argument, as this is a requirement for an advanced degree. If you look at a computer science cirriculum, you will see that most universities will require some assebly language, some C or C++ mid level language and some high level language like Java or C#. A lot of them will require students to create an OS or a compiler as well, thus giving the student the full view of how the computer works.
BASIC is obsolete because computers are so complex these days that to write any program that is interesting or useful, a programmer needs to use libraries, functions, and components that they didn't write as part of thier solution. In BASIC, either you have the code, or not -- you can't just call a function from another .dll file that is on the system.
I think the core of the problem is that the computers have changed in a way that you don't understand how to teach them to a kid without the tools you had when you were a kid to pull from.