Which we already do with TAA and TAA upsampling. Or VRS with TAA if you want with a vis buffer EG
http://filmicworlds.com/blog/software-vrs-with-visibility-buffer-rendering/. Which is not to say you can't do that with texture space shading, just that 99% of the useful stuff here either is perhaps not as novel as it might seem at first glance, or isn't really a win. EG temporal re-use probably isn't a win at all for common worst case, and oversampled shading is just brute forcing what pre-filtering should be doing.
I can see its use for diffuse in VR though, that does seem like it's a win there; and maybe if "lightfield" 3d displays become popular as well. Coherent shading without re-shading where appropriate (diffuse only) where non coherent views are concerned does seem like the real standout feature here, even if that's not yet a concern for most.
I'm optimistic we can use caching for (some) specular as well. If normal angle to viewer does not change much, should be fine even if the stuff we see in reflections is moving.
If the angle is changing too much, we could search for a nearby fragment with a better matching angle.
Though, to get this right, we better separate lighting and materials, so having diffuse and specular irradiance buffers (compromising roughness) to composite with material, meaning we have to do material evaluation and composition for every pixel again, which is a downside.
TSS + caching has huge complexity and requires texture resolution always to be high enough, while SS TA alternatives like such 'software VRS' have minimal complexity and just work. The latter really seems more attractive. At least for now.
On the other side, TSS + caching has an advantage of data locality over SS TA approaches, which is rarely mentioned. Most obvious using RT as example:
If we update a stochastic set of surface patches to cache and reuse, we trace many rays from the same location with similar directions per patch, so rays (but also texture fetches etc.) are more coherent.
If we update a stochastic set of pixels in screenspace and use TA approaches like denoising, rays are scattered all over the place, and we get no nice big packets of coherent rays.
Though, that's all theory. I expected such solutions like 'software VRS' to come up first and turning TSS + caching ideas less attractive. One more source of TA artifacts, but very practical.