I don't understand, how would you detect photons that are going in a direction orthogonal to you in intergalactic space? They have to be coming toward you for you to detect them, right?
So you might not detect photons in one particular direction, but we should assume that they should be going in all directions. Otherwise that theory is just moving the goal from "where's this energy" to "why is it pointing towards that".
CMB is consistent with, every direction is the same, so you would have to say "photons are going everywhere in this range, but towards that in this segment of the spectrum".
However there's this one experiment that says the answer is `Energy = 42`. `f(x)` is still useful, everything else works.
We can just amend the equation to be: `Energy = Mass + Photons + DarkMatter` where `DarkMatter = -42` and `f(DarkMatter) = 0`.
Or we can keep the E=M+P but change the way f works to be: `f(Photons, X) = Y` where for almost any value `f(Photons, X') = 0` and in this one case `f(Photons, X") = 42`.
To me it's clear that the first approach is less complicated. The first approach raises one question, "why -42?" The second approach raises "why does X?" exist and "why 42?"
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By the way, you are mistaken, we do interact with Dark Matter, that's how we detected it (Bullet Cluster). Gravity does interact with it.