"Rigorous" motivation behind the model of transmission line for microwave engineering
For the inductance now, does it physically correspond to the magnetic
  flux between the wires ?


The inductance is what I’d call the leakage inductance i.e. that inductance that remains due to near full cancellation of fields from the opposing currents in the forward and return wires.


  Why don't we add those extra resistor and inductance on the - wire ?


We could if we were considering twisted pair cable but, if we are considering coaxial cable it would be foolish to model the screen as an inductance because, the screen can be shown to possess zero inductance when the coax is driven correctly.

But why over complicate things if complications can be avoided.

Modification of question by op to say: -



  Indeed as I said my wire are really single metallic layer so we cannot
  have some "intrinsic" inductance on those.


There sure is inductance in a sheet or layer.


  More specifically I am interested to this question under the context
  of microwave engineering.


Well, if the RLGC model can be used then it applies to any frequency. However, the term "microwave" is not really clear enough to decide if the model is acceptable due to different modes of propagation.