The Standard Model is extremely well tested experimentally ... it still leaves some freedom where we can search for, especially: asking for field configurations behind Feynman diagrams - for e.g. classical field theory to be effectively described by something close to the Standard Model.
Regarding Gauss theorem, it is not only true, but additionally the real one contains built-in charge quantization - e.g. forbidding half-electron.
We get this charge quantization by interpreting curvature of some deeper field as electric field - this way Gauss law counts topological charge of this deeper field - which has to be quantized ... we also regularize charge to finite energy here (by using Higgs potential).
Sure, there is additional quark structure, which might be only an interpretation - especially that quarks contains only a tiny fraction of baryon mass.
However, getting rid of quarks in a proposed model, we still need to explain the reasons quarks were introduced in the first place - like this "positive core, negative shell" for neutron.
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"The Standard Model is extremely well tested experimentally"
The physics funding pyramid works in such way that both experimentalists and theorists are obliged to keep repeating the above sentence; any person saying otherwise looses funding.
Having been around for 50+ years, the Standard Model should have given some experimentally verified predictions. I challenge you to show any prediction that it successfully gave (e.g. predicted new particle mass, or something else). I went through this exercise of finding its predictions, and all I found were POST-DICTIONS.
I did not go into this topic of bashing the Standard Model in the book, because I aimed to keep its tone positive and constructive.
"Regarding Gauss theorem, it is not only true, but additionally the real one contains built-in charge quantization - e.g. forbidding half-electron"
Understanding the exact reason for elementary charge quantization is a very interesting topic for me. I will contact you to discuss it further.
In Natural Units, the elementary charge value is related to the fine structure constant value. I.e. if one understands reasons for the specific elementary charge value then one knows where the 137.036 number is coming from, and vice versa.
"However, getting rid of quarks in a proposed model, we still need to explain the reasons quarks were introduced in the first place"
Yes, we go into the historic reasons in the book. There was a certain logic to it in the 1950s and 1960s, but it becomes ever more untenable each decade, as experimental contradictions accumulate. You can see the details in the book.
I think history would have been different if the electron's internal structure was more seriously investigated, instead of settling on a "renormalized point-particle" electron and "negative energy" positron hypotheses. That would have allowed scientists to rationally discuss the electron vs. proton similarities and differences already a long time ago.