Cosmological Principle? Cosmological Constant?

This is a continuation of previous posts on Neo-Newtonian Cosmology NC, with focus on how it was overrun by Einsteinan Cosmology EC as prime ingredient of modern physics. 

It is common in physics, when you know nothing, to assume some form of uniformity like homogeneity or isotropy or equal probability, which gives a background for mathematical modelling. As concerns cosmology as the science of the Universe as a whole, this takes the form of The Cosmological Principle CP stating that on sufficiently large scales: 

• The Universe is homogenous and isotropic.
• In other words: There is no special place and no special direction.  

You can learn this from e g the book Cosmology: The Origin and Evolution of Cosmic Structure by Coles and Lucchin presenting modern cosmological models based on Einstein's General Theory of Relativity  GR with the following key message:

• CP was introduced by Einstein with inspiration from Mach's Principle MP stating that Newton's 2nd Law somehow carries input from the large scale structure of the Universe. 
• CP is supported by Cosmic Microwave Background Radiation CMB.

Einstein somehow had to eliminate Newton from the picture and could do so using CP arguing: 

• An infinite Newtonian Universe with constant mass density is an empty universe. (*)

This is because the only solution to Poisson's equation $\Delta\phi =\rho$ in the whole of 3d space with $\rho$ a nonnegative constant, is $\phi = C$ with $C$ constant and so $\Delta\phi =0=\rho$. 

Referring to MP Einstein could further argue that the local geometry somehow was "curved" by influence from the large structure of the Universe, or the fixed stars in the terminology of Mach's time. MP came out as an attempt to explain the Newton Bucket experiment addressed in the post Absolute Rotation: Newton or Mach? showing that Newton was right and so that MP is invalid. 

Even if his arguments were weak, Einstein managed to set the physics community on a train to Cosmology based on GR one of the two pillars of  modern physics. To make this work and get around (*) Einstein had to introduce a Cosmological Constant $\Lambda >0$ (and then retract as his biggest blunder).  

This corresponds in Newtonian terms to expand $\Delta\phi =\rho$ to $\Delta\phi - \Lambda\phi =\rho$ with non-zero solution $\phi =-\frac{\rho}{\Lambda}$ for $\rho$ constant. 

CMB has been questioned as simply noise without relation to any Big Bang hot dense homogenous initial state. 

Summary: The arguments to replace Newton by Einstein as concerns the large scale structure of the Universe are weak. The scientific price to pay anyway doing so, is very large,