I think I'd have felt the same way up until I learned Rust in 2021, and now I just think "I'd rather solve this in Rust" almost always. Rust might have spoiled me for other languages. But yes, in general AoC is definitely a good way to learn a programming language. Since we probably don't need vast numbers of Rust programmers it makes sense to acquire say, Python, or Typescript or something if you're working in some discipline where programming might be useful but is not your core skill.

The initial headline of your front page intrigued me because I had noticed in surveying my own institution (the one where I studied, both as an undergraduate and as a postgraduate, and where I now happen to work) that while most of the undergrad courses of study we offer that require mathematics include at least an opportunity to program, Medicine does not. I reasoned at the time that the Medics have to cram such a large amount of other material into their brief time that maybe there's just no room to teach them to write code if they are to sleep (in my country they certainly won't have time to sleep once they're junior doctors)

This is what I try to do. I solve them all (or nearly, I did one in Python only this year) in Common Lisp (my hobby language of choice), and the last few years I try to tackle them in a second language (Ada, Rust, Python, C++) up to the point that my time is too limited to do both versions (or where I find the second version is adding nothing to my understanding of the language I'm exploring).

This year I used Python as my second language (still plan to finish) but with a strong emphasis on TDD and property-based testing since I'm already familiar, but not fluent, with Python.