Yes, you would be getting some benefits of the SSD by having the program installed there but not as much as if you had your Documents folder on one. But many players have to arrange things the way you have because they don't have a large enough SSD to carry the operating system, the game, and its user game folder. Hopefully in another few years larger SSDs will come down in price and be more standard.
I'm sure you are going to say that your experiences differ, but the only "bad" thing that happens to my active sims when they get MC reset along with their residential lot is that their Dream Managers also get reset so that they start getting beginning of the game types of wishes drawn again until things settle down. But for me it never disturbs their currently promised wishes, their behavior, or their appearance unless something was already wrong with the sims and their wardrobe/CAS assignments. I hate doing this too as it's disruptive to gameplay unless I am about to switch active households in a rotation anyway and put it off as long as I can, but still do so every few sim weeks in the middle of the sim night when it seems feasible.