While the energy is conserved, mass is not conserved. While the total energy of the resulting photons is equal to the total energy of the initial particles, it is no longer expressed in terms of mass. If no mass, no gravity.
I still can't accept this. I feel like energy is being lost in the form of gravitational potential energy or whatever. I feel like this is a quirk of our limitations on understanding.

idk, once we thought that gravity was a force, carried by a particle, but now we understand it as a consequence of warped spacetime. Maybe the photon plays a similar role... maybe electromagentism isn't a force, maybe it's a consequence and we're just doing it wrong.

It seems logical to me that, if photons are massless but have an energy value, anything emitting photons is losing mass, and therefore gravity.

I feel like if a photon is a particle, then it must have a non-zero mass, just perhaps a mass so small as to be immeasurable. Otherwise, I'm inclined to think the fate of the universe is graviational decay, as matter slowly decays into photons.

Can photons turn into matter? A quick google search seems to imply this is theoretically possible. If two photons collide, then we have an electron and a positron. That's two particles with mass that interact with one another graviationally, created from two particles that apparently don't interact with one another gravitationally.

That "missing" gravity must exist somewhere in some form, imo. Maybe in the case of the photon, gravity is turned into electromagnetism. Maybe our missing "mass" is how we can prove gravity and electromangetism are one and the same.

Well this is a nice start to my sunday. I'm still in bed with a spliff, talking shit about the most complex of subjects. All that's missing is tea...