It depends on what you mean by "light loses energy over cosmological distances". See below.
> We already know that energy isn't conserved at those scales.
This suggests that what you mean by "light loses energy over cosmological distances" is that the universe is expanding while the light travels, and in an expanding universe, total energy is not conserved. That is true, and that is the redshift due to the universe expanding--it's not something different.
If, however, you are working from the hypothesis that the universe is not expanding, then energy is conserved even over cosmological distances, so I don't understand what you mean by invoking "energy isn't conserved" as an explanation for the redshift.
If you're referring to the "tired light" hypothesis, that's been known to be unviable for decades.
Actually, turns out the math was right with a cosmological constant: that's how the accelerating expansion of our universe is explained. Einstein actually blundered twice: first by putting in the constant for the wrong reason (because he wanted a static universe), but then taking it out again when it turned out that reason wasn't the case (when the expansion of the universe was discovered).
If you just look at how to derive the Einstein Field Equation of General Relativity from first principles, the constant should be there; it isn't an add-on to General Relativity at all, it's part of it. It's just that there's no way to know from those first principles what its value is. That we had to figure out from observations.
Thanks for your point about the constant being actually required. I do not understand the math, but is this similar on how integrals always have a constant as a free parameter that need to be determined by other means?
I assume that Einstein originally set the constant to exactly balance the expansion, but later set it to zero. In bot cases you are picking arbitrar values but the actual value need to determined by empirical observeations.
I wouldn't go that far: Rather, adding it doesn't violate any of the heuristics used to come up with the field equations or action. So to avoid bias, one should keep it around. However, in the absence of observational evidence to constrain its value, it's also justified to start any investigation with its value assumed 0...
