Bash functions are very useful when you want to manipulate the state of the shell in some way. That is, you write a function for it and stick that function in your .bash_profile. (Unless ofc an alias would be able to perform the job in which case one should just make an alias instead.)

Beyond that, I have been in many situations where standalone shell scripts make the most sense for a task and in which case bash functions have helped me organize the code such that it is both more readable and also so that I don't have to repeat sections of code multiple times within a single script.

It all comes down to personal experience and preference, I think.

I wrote sh for this very reason http://amoffat.github.io/sh/ This lets you use a programming language, instead of a shell language, to solve programming tasks.

Actually, this is exactly the sort of guide I've been meaning to read, since I'm inclined to take the opposite view.

Too often, I think, my task is probably sufficiently simple that it could be a nice portable obviously-a-script Bash script rather than Python/whatever.

It's useful to be able to write functions for your shell. For example, I have a function up, which moves up n dirs.

Even if that is true, it doesn't mean you should not cleanup and organize the bash you have "today" and will port "tomorrow". In the meantime your bash will be better organized and more maintainable.

Please list other backwards-compatible interpreted languages installed by default on dozens of operating systems and platforms spanning 26 years.

Build scripts for various things are often done in bash, and functions are quite helpful there (unified cleanup routine, for example).

Just because you can do something in <pet-language-name-here>, doesn't mean it's best done in <pet-language-name-here>.

Possibly, but bash functions can still be quite useful even in a relatively simple script.

Your point is valid, that bash should be avoided as processes become increasingly complex. But there is still room for bash. How much room depends on what you are trying to do.