I think Dijkstra's point was specifically about uni programs. A CS curriculum is supposed to make you train your mind for the theory of computation not for using specific computers (or specific programming languages).
Later during your career you will of course inevitably get bogged down into specific platforms, as you've rightly noted. And that's normal because CS needs practical applications, we can't all do research and "pure" science.
But I think it's still important to keep it in mind even when you're 10 or 20 or 30 years into your career and deeply entrenched into this and that technology. You have to always think "what am I doing this for" and "where is this piece of tech going", because IT keeps changing and entire sections of it get discarded periodically and if you don't ask those questions you risk getting caught in a dead-end.