SR was an invention to explain observable "phenomena", following the interpretation of the results of the Michelson Morley experiment of 1887. Prior to this exp., there was the aether, which was assumed to exist because light was shown to be a wave (Poisson 1818); and all waves require something to wiggle through.
The MM Ex apparently proved there is no aether, and therefore no wave medium for light. Therefore, the photon was invented, EXCLUSIVELY to explain how light gets from the Sun to Earth. In the whole e-m spectrum, light was the only particle, with all other frequencies being waves.
Even today the terminology will not go away, because too many observations are explainable only by wave theory. The wave/particle "duality" theory is another invented crock.
Of course bodies of matter can vibrate; but this is hardly a "wave function". And certainly waves "impact then disappear" just like water waves crashing on a shore; but this does not give the wave entity itself matter status. It is the WATER that contains the mass in this particular application of the kinetic energy formula.
So the light particle is said to have "momentum", because it does impact then disappear, tranferring energy to a solar cell, skin or whatever. But because it disappears; and space is said to be without a wave medium, light particles are said to have zero rest mass. Its momentum is designated by "p", because it supposedly has no mass. Everything else has its "momentum" described as Kinetic energy = mv^2/2.
But if light is a wave, there is no need for any bizarre massless particle.
Today there is no sort of theoretical SUBSTRATE upon which all the forces and energies affecting matter and electromagnetics can play out. The MM Ex and the Non-Skewed Light Waves experiment took the aether from us. But both experiments are fatally flawed. They are both insensitive to the aether "wind", and could not detect it if it does exist.
This is why, in General Relativity, Einstein geometrically warped empty space in his "explanation" of how gravity works.
Today, physicists like Hawking and the rest, call it anything but "aether", even tho' they KNOW their observations prove something fills space. Hawking likes to show the cannon ball rolling around on nothing. Greene repeatedly calls it the "fabric of space". Then there is the Higgs field, Zero Point Energy (not specified as "particles", Dark Energy (no description whatever), and Dark Matter (never seen), Expansion Reacceleration's "Quintessence", 5th Force, and Inflation's energy-from-nowhere.
Add to that no known mechanism for having converted the energy of Inflation into the various things like protons and electrons, which have completely different properties.
Who says anything had to be created? There is no rational explanation for existence known to us.
I don't understand your remark about the average value of all energy in empty space being zero. First of all; what is this "all energy"? Is it particles, waves or something else? How is it able to nullify itself; yet still exist? Only wave energy can do that, and waves require a medium.
Secondly; it is "measured at ~3K", which presumes a differential between two places. How are we able to do this, if it fills all empty space? We must have access to an enthalpic pile in order to generate the reference point, using say, liquid helium. The Sun is in empty space, as indeed is Earth. There is no such thing as "deep space", there is simply space.
Third; Since you suggest energy fills all space, then you have provided an energy source for gravity, Internal Heating of Celestial Bodies and the Auto-Ignition of Proto-Stars, among many other things; like Static Cling and Particle Accelerators.