I think it's hard to do robustly, though that particular footgun may be removed through other means eventually. In the meanwhile, I believe that if you're going to drop any part of the payload you should use another catch_unwind! (or leak the payload). But doing this is rare. As it turns out, reasoning about panics is hard, even in code explicitly about catching panics, because of their often-invisible nature.
That said, you're also getting push-back because it's not idiomatic Rust and it's (excuse the pun) an exceptional code pattern, not an expected one. It is not what you should reach for as part of normal error handling, and it makes addressing the error cases invisible and forgettable -- anti-patterns in Rust.
So when an Rustacean reads "[As I Rust beginner I recently learned that panics] may be worth considering an an alternative to Result", they're probably going to jump in and correct you. Not just to be pedantic, but also to guide you toward idiomatic Rust and away from footguns.
More generally, this feels like one of those mid-level issues, like self-referential structures or falling back to raw pointers (or falling back to unsafe generally). Are they possible? Yes. Should you learn them and should we have better material about them? Eventually you should and we definitely could use some better or centralized material on some topics. Are they what you should be reaching for in your first projects and while you're still getting a feel for the language? Almost certainly not.