Until now I've run in strong stability/motion control shoes, after being advised that I was a severe pronator. I've not had any injury issues traceable to shoes but I have at times found them to be a bit stiff and clunky.
I had another gait analysis done recently, at Decathlon. Not so much a gait analysis as a look at my footfall and ankle flex in a variety of shoes from "natural" to mild stability. The results were odd. In the "natural" shoe I pronated a little but they felt sloppy underfoot. In one mild stability shoe there was also a little bit of pronation but in another there was none that we could see. Both felt and fitted fine.
That said, I suspect my gait may have changed over the years. I think I used to be more of a heel striker but I now aim for midfoot to forefoot strike and slip back to heel when I'm tired.
So I'm not quite at the "any shoe will do" stage but the lesson I took out of this was that in future I'll pay more attention to the gait video than to the category I'm put in.