Bitcoin as a core subject? Well in my opinion I would say cryptography as a core subject rather. Then students or pupils will be able to get a proper understanding of how the crypto space works especially in the case of Bitcoin. For some time now some schools already offer such subjects to their students however most of the time as a branch under one of their networking or programming subjects. I think if it was a full subject it should be divided into cryptographic programming and crypto economics.
I want to echo your words. Bitcoin is just one cryptocurrency. Instead of explaining how Bitcoin works, they should teach how cryptography and blockchain technology work. Also, it is advised to teach the importance of privacy. Now, let them decide if they want to know more about Bitcoin. In my country, the government introduced a new subject named ICT back in 2013, and it's one of the mandatory subjects for the 6th grade. Unfortunately, they don't teach about cryptography in ICT classes. Instead, they start CSS, HTML, understanding binary, and other things like that. I did not have a chance to check the higher grades books. But I hope they have included cryptography and blockchain technology as well.