Actually, at earlier times the "beam" of flux from a distant object had even less energy, because the rate at which objects separate is slowing down with time. So a distant object starts off being redshifted out of the visible universe and then enters the visible universe at very high redshift and now has dropped to the present value. But, there is more to the story than just ordinary Doppler motion. The photons do work on the universe (note there is a term for the pressure of relativistic particles in the Friedmann equation) and therefore lose energy. Where does it go? Well, you can think of it as going into potential energy. If the universe collapses (it won't, but if it did), you would get that energy back again.
This issue is briefly discussed by Sean Carroll in an essay "Energy is Not Conserved." Here is an extract:
... We all agree on the science; there are just divergent views on what words to attach to the science. In particular, a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.” Which seems pretty sensible at face value.
There’s nothing incorrect about that way of thinking about it; it’s a
choice that one can make or not, as long as you’re clear on what your
definitions are. I personally think it’s better to forget about the
so-called “energy of the gravitational field” and just admit that
energy is not conserved, for two reasons.
And he gives his reasons for preferring to say energy is not conserved. In particular, he mentions that this is an issue of translation, not of physics.