The actual "why" is the author did it for fun, there's basically no purpose to it. I can try to explain it though:
Interacting with file systems can be generally summed up in a handful of basic operations. Two of the most important operations are open, which asks the filesystem if it has a file of a given name, and read, which reads the contents of that file. FUSE is a Linux wrapper for writing virtual file systems by implementing these basic operations. Here open, instead of taking a filename, is telling the program what command to run and read, instead of returning the contents of a file is returning the output of the command.
I can understand if you want to do something wacky with FUSE. Something like mounting a PostScript or JSON file, and using the filesystem interface to observe and modify the contents. Or something else that is vaguely hierarchical.
I just didn't see any "reasonable" mapping for running a series of commands to a filesystem.
It's mainly for fun, but to find cases where it might be useful, think about symlinks into this filesystem. `ln -s /bashfs/somescript.sh /etc/hosts` and then your hosts file can be dynamically generated without any changes to programs that read it. It can be a clever way to sneak dynamic behavior into contexts where there would normally just be a static file.
The "why not" is pretty obvious so that doesn't really answer the question.
But anyway the "why" is equally obvious - for fun! There's no way anyone reasonable would consider this useful or even sane so it must just be for fun, or to learn about FUSE.
Interacting with file systems can be generally summed up in a handful of basic operations. Two of the most important operations are open, which asks the filesystem if it has a file of a given name, and read, which reads the contents of that file. FUSE is a Linux wrapper for writing virtual file systems by implementing these basic operations. Here open, instead of taking a filename, is telling the program what command to run and read, instead of returning the contents of a file is returning the output of the command.