No, its not possible to remove the viewing direction from a BRDF that requires it without breaking its appearance.
Yeah, I realize that. My question, again, is which ones these are, and whether there are any that have the qualitative properties that I'm looking for where the "amount" of light received (represented in a single white directional light as dot(normal, lightdirection)) is sufficient.
It's obvious that there are materials where this is insufficient, but I still suspect (hope) that there is a material that meets my needs because a) there materials I'm trying to mimic don't "look shiny" and b) the key qualitative difference between them and ideal Lambert shading seems to be that the amount of light emitted toward the viewer is reduced when the surface is angled toward the viewer and increased when the surface is angled away.
I think maybe you're saying that Oren-Nayar, in particular, cannot be implemented without having the light direction. Are you, and if so, what about the various "Minnaert" shaders, etc.?
You might also be saying that the effect I'm looking for will never be possible (maybe because of conservation of energy, etc.) at least in a reasonably physically-accurate way. Are you, and if so, can you provide some more insight so that I can assess exactly what is and isn't possible? On a basic level, it seems that I could approximate what I'm looking for with some kind of "rim light" shader that is blended (multiplied) with the diffuse value.
In these cases, a lot of engines use baked lighting under multiple basis vectors, such as RNM or SH maps, and there is also directional lightmapping, where you have a bake of the direction to the most dominant light per pixel.
I'm aware of that also, but that's also not what I'm looking for at this time.