Most of the time the information would be roughly as useful as a C compiler telling you what loops it will unroll. Game-specific optimizations basically means "take the whole rendering pipeline, make optimized shaders like ASM, reorder, parallelize, cut excess calculations, use conditional simplified algorithms and whatnot to achieve essentially the same output". It's not surprising that most of these tricks will work on a game built by the same engine, but it doesn't extend to the general case. So it wouldn't really be very useful, instead of "photo" or "fps" the profiles would basically be one per game.
I remember at some point the AMD open source developers said that they didn't have manpower to optimize for different workloads, so they were going with a simple structure using only one algorithm. They guesstimated that they could typically get 70% performance, simply because past a certain point making some things run better would make other things run worse. At the time they were more busy making it work at all though, but it might have been based on experience from Catalyst. Remember there's a pretty big gap between DirectX/OpenGL and actual hardware, at least before DX12/Vulkan/Mantle.