I think this has to do with the default path settings. It starts out with the connection storage as “Personal Database” which is indeed the documents folder. 

Personal Database (default): The connections data file is stored and encrypted on the user's local system. Connections are available only to the user.

(pictured is the latest 25.1 version)

That answers the “how” of the question

My question is “why”? Why did the software authors make this design decision?

Because the files in the shared folder (Documents/FME) are user resources : things the user might want to easily view, edit, add, or remove.
 

For example, Documents/FME/Transformers is where custom transformers go, whether you've created them yourself or downloaded them from FME Hub. FME usually handles this automatically, but you might also want to do it manually (download a transformer from the Hub and place it in the folder yourself).
 

The AppData folder isn't really meant for end users to poke around in. It's more of a system/internal-use location. So unless Safe Software completely wrapped and abstracted away the shared folder management, it makes sense to keep this stuff somewhere the user can get to easily.

​@nicholas 

FME often stores files in the "My Documents" folder, or a subfolder within it, due to default settings and the need for user-specific storage. Specifically, FME's default connection storage is set to the user's Documents folder, which ensures connections are unique to each user. Additionally, FME uses a "My FME Workspaces" subfolder within "My Documents" as a default location for saving workspaces, providing a convenient place to organize FME projects. 

May be this could throw some light on why the OEM decided to have it that way!

https://docs.safe.com/fme/html/FME-Form-Documentation/FME-Form/Workbench/options_default_paths.htm