In the wake of the Shellshock issues, a lot of people started asking why Bash even had a feature to import functions from the environment. The obvious answer is to allow subshell Bashes to inherit functions from parent shells. Now, you can come up with some clever uses for this feature (eg to pass very complex options down from parents to children), but as it happens I have my own views about why this feature probably originally came to exist.

Let us rewind to a time very long ago, like 1989 (when this feature was introduced). In 1989, Unix computers were slow. Very slow. They were slow to read files, especially if you might be reading your files over the network from a congested NFS server, and they were slow to parse and process files once they were loaded. This was the era in which shells were importing more and more commands as builtins, because not having to load and execute programs for things like test could significantly speed up your life. A similar logic drove the use of shell functions instead of shell scripts; shell functions were already resident and didn't require the overhead of starting a new shell and so on and so forth.

So there you are, with your environment all set up in Bash and you want to start an interactive subshell (from inside your editor, as a new screen window, starting a new xterm, or any number of other ways). Bash supports a per-shell startup file in .bashrc, so you could define all your shell functions in it and be done. But if you did this, your new subshell would have to open and read and parse and process your .bashrc. Slowly. In fact every new subshell would have to do this and on a slow system the idea of cutting out almost all of this overhead is very attractive (doing so really will make your new subshell start faster).

Bash already exports and imports plain environment variables, but those aren't all you might define in your .bashrc; you might also define shell functions. If a subshell could be passed shell functions from the environment, you could bypass that expensive read of .bashrc by pre-setting the entire environment in your initial shell and then just having them inherit it all. On small, congested 1989 era hardware (and even for years afterwards) you could get a nice speed boost here.

(This speed boost was especially important because Bash was already a fairly big and thus slow shell by 1989 standards.)

By the way, importing shell functions from the environment on startup is such a good idea that it was implemented at least twice; once in Bash and once in Tom Duff's rc shell for Plan 9.

(I don't know for sure which one was first but I suspect it was rc.)