As a person who was taught the “traditional” way, I feel that Aaronson’s disparagement of it misses—and the title tellingly omits—an important reason for it: that it tries to explain why quantum mechanics is mechanics. For that, you actually do need to know Hamilton–Jacobi, and ideally also know how to get the eikonal equation from electrodynamics, perhaps even understand high-frequency (Liouville–Green or, with a bit of abuse of language popular among physicists, JWKB) approximations in general. Same applies somewhat less poignantly if you’re not looking for motivation but are still planning to do QM to things in, y’know, continuous physical space.

The realization, apparently due to quantum computing people, that you can get away with not doing QM to things in continous physical space and still understand quite a lot of fun and useful QM stuff is very much valuable; you absolutely can build good courses that way. It’s just that I think that the pedagogical problem of laying out this general “quantum dynamical systems” approach in a compatible and not terribly redundant way to include the things learned a “quantum mechanics in space” course—which is absolutely required if e.g. you want to move on to QFT in solid-state or high-energy physics—is unsolved and to a large extent even untried. (Susskind’s semi-popular book is a notable exception, but I don’t feel he managed to pull it off.)

And, as usual, calling the traditional approach “historical” is a huge stretch. The standard QM course doesn’t talk about the founders’ (valid but extremely clumsy) approaches to relativistic corrections to the hydrogen spectrum any more than the standard calculus course talks about Newton’s early forays into algebraic and (what would come to be called) tropical geometry. (Or the standard programming course talks about native–bytecode interworking in the AGC, but even the most academic of programming courses are rarely branded as historical.)