The answer to this very good question seems to be favored by a large amount of users.
Yet it seems to imply that the constancy of the speed of light and its finiteness stems from the underlying space-time symmetries.
First it says:
... let me note that speed itself is a coordinate system dependent concept. If you had a bunch of identical rulers and clocks, you could even make a giant grid of rulers and put clocks at every intersection, to try to build up a "physical" version of a coordinate system with spatial differences being directly read off of rulers, and time differences being read from clocks. Even in this idealized situation we cannot yet measure the speed of light. Why? Because we still need to specify one more piece: how remote clocks are synchronized. It turns out the Einstein convention is to synchronize them using the speed of light as a constant. So in this sense, it is a choice ... a choice of coordinate system. There are many coordinate systems in which the speed of light is not constant, or even depends on the direction.
How is agreeing on the speed of light a choice? If we didn't accept a priori its constance, what sense would it make agreeing on a value? You would end up with very different conclusions about the world depending on how fast was light speed locally for you.
Further it says:
...It is because of the symmetry of spacetime that we can make an infinite number of inertial coordinate systems that all agree on the speed of light. It is the structure of spacetime, its symmetry, that makes special relativity...
and ends with:
...The modern statement of special relativity is usually something like: the laws of physics have Poincare symmetry (Lorentz symmetry + translations + rotations)... Not everything is relative in SR, and speed being a coordinate system dependent quantity can have any value you want with appropriate choice of coordinate system. If we design our coordinate system to describe space isotropically and homogenously and describe time uniformly to get our nice inertial reference frames, the causal structure of spacetime requires the speed of light to be isotropic and finite and the same constant in all of the inertial coordinate systems.
From what I understand, this would seem to imply that you have freedom in choosing your coordinate systems and this would yield different results for the measured speed.
While it is equivalent to derive the constancy of light speed from the symmetries of space-time, as opposed to the inverse process, I don't think it yields the same result in the construction of knowledge. The former order would imply that light speed can vary, depending on the local space-time properties, and we are choosing a convention in which the value is the same. This would mean that the comparison of light speed with other, say sound speed, would be region dependent, since the latter depends at least on the medium properties if not also on space-time.
However, the second one, where light constancy assumption yields the symmetries, would imply that the local space-time properties however altered, will always hold the light speed, which seems to me more natural and consistent with reality.
My question is then: Are the answer's assertions correct? If so, where am I misunderstanding?