What important problem in this domain does the author think plain text uniquely solves? I'd say that the arguments aren't specific to education, and that they're also pretty weak.
Remember that one of the major breakthroughs of the World Wide Web was that HTML meant documents were no longer plaintext.
You could replace "plain text" in the article with "non-binary", and it would probably make more scence. Markdown is also not plain text in the most strict sense. Or HTML is plain text in a vague sense. In the end, what really matters is how easy it is to build parsers and tools for a format. Being non-binary is a huge plus. I think that was the point of the article, and I agree with that.
I don't think anyone would claim that HTML was easy to parse, would they? It took decades for the HTML5 consensus to emerge.
I like text-based formats, but I'm not convinced that "Being non-binary is a huge plus" for parsing. With binary formats you can assume that documents are generated by a tool, which is at least trying to be compliant with a spec, so barfing on noncompliance is more acceptable. With text you have to be prepared to cope with any kind of rat dance imaginable.
Parsing semistructured text as markup is a problem solved over 30 years ago [1].
SGML has the SHORTREF feature which allows custom Wiki syntaxes such as markdown, but also casual math. It works by applying a context-dependent (parent element dependent) mapping of tokens (such as the `_` token for markdown emphasis) to replacement text (eg. the `<b>` start-element tag). Within the `<b>` context, the `_` token is mapped to the `</b>` end-element tag, in turn, ending the emphasis. In combination with tag omission/inference (such as in HTML) and other markup minimization and processing features, SGML is a quite powerful plain text document authoring format.
We may be talking about different things. Parsing valid, standard-conforming HTML/Markdown/whatever is a solved problem. Getting multiple parsers to deal with arbitrary tag soup, authoring errors, variously-supported extensions etc in a consistent way is a lot uglier. The problems may be commercial/political/educational/organizational rather than technical, but that doesn't mean they aren't real.
Remember that one of the major breakthroughs of the World Wide Web was that HTML meant documents were no longer plaintext.