Logic Missing for Dumping Newton's Mechanics

Did Einstein seek to put the left foot in the right shoe? 

The triumphs of modern physics are presented as Quantum Mechanics QM and Einstein's Special/General Theory of Relativity SR/GR developed 100 years ago, but the success story is shadowed by the realisation that QM and SR/GR are incompatible with no reconciliation in sight. This is troublesome and contributes to the present crisis of modern physics. 

While Newton's Mechanics NM and QM are fully compatible, a modern physicist insists that NM has to be replaced/revised by SR/GR, and so it is natural to ask what is wrong with NM? An answer is given in Einstein's famous article from 1905 introducing SR with title:

• On the Electrodynamics of Moving Bodies.    

Einstein forms SR as an expression of the Lorentz Transformation LT connected to electromagnetics/light described by Maxwell's equations and compares it with the classical Galilean Transformation GT connected to NM. Einstein then declares that since NM does not fit LT, it is necessary to replace NM by SR fitted to LT. He does not say that because electromagnetics does not completely fit with GT, it has to be dumped. Only NM has to go.

But the logic is missing: LT is fitted to electromagnetics, while NM is not electromagnetics. There is no good reason to throw out NM because it does not fit with something fitted to electromagnetics. There is no good reason to throw away your right shoe because it does not fit your left foot! 

In any case this was what Einstein did and so concluded that NM had to be replaced by relativistic mechanics based on SR with all sorts of strange effects such as space contraction, time dilation, and relativistic mass increasing with speed.  

Returning to classical physics in the form of NM + electromagnetics and giving up relativistic mechanics can open to get out of the present crisis. Anybody willing to try? 

An alternative to SR compatible with NM is presented in Many-Minds Relativity.

Bear in mind that the difference between Einstein's relativistic mechanics and Newton's mechanics is viewed to be exceedingly small, so small that detection is virtually impossible. There is a heavy price to pay for replacing Newton by Einstein and the gain appears to be virtually zero. GPS does not need SR/GR to work.  

Why insist to keep SR/GR before NM arguing that Einstein was smarter than Newton, when the negative consequences are so huge and Einstein's genius can be questioned on so many good grounds?