Because the shift is linear. And they believe that it's a Doppler shift, like a sound wave.
Doppler shift is linear.
But light does not Doppler shift. The expanding cosmos is an measurement illusion.
But no one knows this.
That shift is a natural occurrence with light propagation. It's a duty cycle shift.
It's simple motion mechanics. And no one knows that either.
The Doppler shift of light is observed on a regular basis. I see no reason to posit the "tired light" theory. I've only heard the term "duty cycle" used by engineers, concerning man-made machines. I also know my physics mechanics.
In short, I don't know what you're telling me here, and it's not because I'm uneducated. Frankly, I'm starting to think I'm in the wrong room. I can't see how anybody here is addressing the question I asked. For what reason must we assume Hubble's Law is linear? If there is no good reason, then we should consider alternatives also. The tanh version seems to predict the tensions we now have with the linear version.
I am ignorant of any compelling reason that Hubble's Law must be linear ‒ so why not pick something else that fits the facts better, and maybe gets rid of some ad hoc assumptions?