You should look into the Frame Generator "Reuse" feature. This allows a frame member file to be used more than once if it is repeated, rather than placing a separate part file at each location. This is much more like the way Inventor would treat normal part files. The feature is relatively new (was introduced in Inventor 2015).
Using this method, you would have ended up with only one part file instead 16 duplicates. If your current situation bothers you enough to justify changing it, you can delete all of the frame members but the first one, then use the Reuse feature to sort everything out.
Regarding the folder structure, there is nothing that keeps you from moving those part files out of the Frame folder (they follow normal Inventor file linking rules, so as long as they are within your project file's Workspace you should be fine). However, as far as I know there isn't a way to make Inventor stop saving new frame members to the Frame folder. So if you do this reorganization, you'll want to wait until near the end of the project to avoid having to shuffle the files around again every time you add or change a frame member.
