What is the logical reasoning behind speed of light being the upper limit too given that it is constant, independent of relative motion? Basically, using the two postulates of special relativity and other physical arguments, we can arrive at Lorentz transformation where gamma has to be real and thus we conclude any relative speed between two frames must be less than c (speed of light). I consider this to be rather mysterious as I had not expected this to happen after accepting the 2nd postulate.
I am still not convinced with the argument of deriving this major claim given that we already have one (2nd postulate); I feel there must be a logical way to deduce this (with no mathematics) which I can neither find anywhere nor think for myself.
So, what I am asking is the method to arrive at the conclusion using physical arguments, the 2 postulates and logic (no mathematical equations) only.
 A: There is a simple argument that shows that the relative speed of two inertial frames cannot exceed the speed of light.
Suppose we have two observers A and B travelling at constant velocity, but whose relative speed is greater than the speed of light. A emits a photon towards B. In A's reference frame B is moving away faster than the photon, so the photon can never reach B.
But using the second postulate, the speed of light is constant in B's reference frame (so the speed of the photon is not affected by A's motion). So in B's reference frame the photon is approaching B at the speed of light and must eventually reach B.
By the first postulate the photon cannot reach B in one reference frame and can reach B in another reference frame. So our initial premise, that the relative speed of A and B is greater than the speed of light, must be incorrect.
A: "given that it is constant, independent of relative motion"
It is not. The frequency and the speed of the light pulses VARY PROPORTIONALLY for the moving observer in Doppler https://www.youtube.com/watch?v=bg7O4rtlwEE, in violation of Einstein's relativity. The wavelength (or distance between subsequent pulses) obviously remains constant:
"Thus, the moving observer sees a wave possessing the same wavelength [...] but a different frequency [...] to that seen by the stationary observer." http://farside.ph.utexas.edu/teaching/315/Waveshtml/node41.html
