Relativistic frequency shifts can be understood as kinematic effects, namely orientation of photon 4-momentum relative to emitter and absorber 4-velocities.

Now, spacetime geometry might be such that there exists space/time decompositions that allow us to attribute the shift to specific physical effects (relative velocity of emitter and absorber in case of special-relativistic Doppler shift, time dilation in case of gravitational shift in Schwarzschild spacetime, spatial expansion in case of cosmological shift in FLRW spacetime), but from the perspective of spacetime geometry, these are just specific instances of a general mechanism that is agnostic to such attributions.

Don't take this the wrong way.

If you can't explain what's in your head in plain English in answer to a question that was asked in plain English then there's not much point in answering.

I'm not getting the impression that you've answered my question, I'm getting the impression that you don't know how to answer my question.

I'll try again:

General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is due to time dilation or spatial expansion, we can just do the math. But if we're lucky, we can find a way to split up space and time that allow for such intuitive interpretations. However, that's window dressing, so to speak.

All this assumes that the spacetime in question is already known, but that's how it actually happened historically: Friedmann and Lemaitre derived their solutions by imposing certain symmetries on the problem. From that, you can derive observations like redshift (Lemaitre had already done so by 1927, ie two years before Hubble published his paper), which you then compare to observation in order to fix the parameters of your model, or scrap it if it cannot accomodate observation.

As far as I'm aware, at no point in time did a physicist sit down and think "I wonder, what's the best way to incorporate redshift into my model, time dilation or spatial expansion?".

Much better!

Now, if there is a failure to understand your answer the reason why lies with me :)

If this temporal expansion or contraction produces redshift in the exact same way, and you can fit it into Relativity with the appropriate math, well, six of one, half a dozen of the other — until such point as we understand some discrete mechanism underlying the operation of the universe that would be affected by the expansion of one rather than the other: minimum time steps, minimum distances, proceeding from individual bits, increments of information. (Such a thing is theorized, but observing it is on no one's radar today, so good luck.)

(If it doesn't fit, then it's just wrong.)

If this is an accurate conceptual model: https://www.esa.int/Science_Exploration/Space_Science/What_i...

I have this odd notion that the universe has stayed the same "size" (since inception) and that the parameters of the universe and the amount of matter/information has changed over time.

The impression we get (from our perspective) is that of an initial singularity, a period of hyper inflation, and then the expansion we have now.

Probably bollocks but I'd like to know why it's bollocks.

That's the same thing that's always bothered me. That physicists never seem to discuss global time dilation - which also to my layman's eyes seems like a simpler explanation.

Time everywhere is slowing down (speeding up?) Which it's why the expansion of space seems so perfect to neither accelerate nor decelerate.

Thank God there's someone else. I mean, to me, the idea is so moronically obvious (I had the idea about 15 years ago) that there must be some obvious answer why space-boffins insist that it's space that's doing the jiggling rather than time -- even though we've been told that since Einstein we ought to view the dimensions we inhabit as the spacetime (time is just another dimension) continuum.

My gut tells me that the layman's model I have of the universe precludes me from having a handle on why the idea is dumb. I console myself with the knowledge that at least I'm not so dumb that I think the idea is l33t and the whole scientific community are morons. Still, it'd be nice to have an answer.