Because it's trash. Things decay into what they decay into. For example a neutral pion usually decays into two gamma photons in about 8.4 times ten to the minus seventeen seconds. It sometimes decays into one gamma photon and and an electron and a positron, but that's fairly rare, see
wikipedia. You could arrange things so thet the electron and positron annihilate into two (or more) gamma photons. However two (or more) gamma photons will happily zip through space for a million years without magically "decaying" into a pion.
Farsight, the point is:
a) You seem to think that "p-pbar annihilates to photons" is:
a') true, and
b') an important statement about the nature of the strong force.
a'') You argue it's "true" by pretending that
neutral pions might as well be photons, because that's what the neutral ones decay to, and the charged ones decay to stuff that
you could re-collide later to get photons. Including, um, the neutrinos---well, technically yes, but good lord.
Whatever. More importantly.
b'') Your rearrangement
cannot possibly contain any information about the strong, weak, or electromagnetic forces. Because it's a tautology. It's true for
any particle whatsoever, known or hypothetical---muons, buckyballs, W-bosons, Higgs bosons, axions, charginos, technimesons, Z' bosons, the "video quark"---for any X, it is true that X-Xbar annihilation leads to (a) photons, (b) things that can decay to photons, and (c) pairs of things that could be made to annihilate to photons. It's just a conservation law.
Imagine someone saying "I understand the number 16 better than anyone else. Here's a hint: divide sixteen by all of its factors (2,2,2, and 2), and what do you get?
One."