Hmm.

If photons have non-o mass, then the Law of Conservation of Electric Charge would break down.
Also, the force between charges would diminish at a greater rate than the 1/r^2 relationship we observe.
The gauge invariance in Quantum Electrodynamics would no longer hold.

Probably more.

I say this to convince you that photons are highly likely to have 0 mass, since these theories are quite robust, and have been experimentally confirmed for decades.

The upshot is that when matter changes form into energy, that mass is no longer expressed as mass, and does not influence things gravitationally.

So the idea that mass - I.e. gravity sources - can be destroyed is fully consistent with the Standard Model.