Rick, no telling if my answer will be satisfying, but here goes. I never use Tree Share to bring down media items, but rather download separately and manually link. I do the same with Family Search, Find My Past, and all the rest of the paid repositories. I separately maintain my Ancestry tree, and ne'er the programs shall meet! Lots of extra work, to be sure, but I'm insulated from programming decisions made by Ancestry and indeed, Roots Magic. My manual implementation of repository connection ensures data and filing integrity and avoids the problem you've mentioned of finding and renaming files brought in by the various APIs.
The reasons for any particular subfolder structure (indeed, even having one at all!) lie with the desires and processes of the individual family historian. Use what works for you, not only in filing, but also in source lumping, citation format and every other aspect of this fantastic pursuit! Hope this helps, I'd be delighted to explain further.
I like your idea of having a separate sub-folder for each person, or non-person specific topics such as cemeteries etc. This would make searching more simple. (by the way - while testing today I noticed that RM will handle movement to a sub-folder without requiring a re-link to the media.) I have been using Tree Share to bring in items to RM from Ancestry, but it usually causes so much trouble with having to rename and relink that I might as well start saving my own media and do it right to start with. I use a person centric syntax for naming media (Last, First, Middle, (Maiden) - (bxxxx) - Description). I also have a list of standard descriptions (birth, death, marriage, military, etc.). These work well, and I think the addition of subfolders will also help.The more I can do to keep this simple and fast, the better.
Thanks for your input.