Jonathan
Never mind about stars that are a long way away. You see everything after a time delay, because what you receive is a photon based representation of what actually occurred, and it takes time to travel from where the photon interacted with what occurred to an eye.
Einstein's argument is, obviously, not about the subsequent processing of what is received. Nowhere does he allude to this, and no physical theory can explain physical existence physically, based on the vagaries of the way in which sentient organisms process physical input.
Einstein's argument is also not about how observational light travels at a constant speed. Obviously, to all practical intents and purposes it does, unless during travel it is impeded by some particular circumstance. We certainly cannot identify the actual speed on every occasion, though there must be one. So approximating it to a constant cannot be an issue.
Where Einstein's argument is wrong is in his failure to differentiate the photon based representation we receive (aka light) from what it is a representation of (aka reality). The c that he is referring to as constant is, because of this conflation, the time constant, which he is asserting, incorrectly, is the time constant for physical reality. That is why he measures distance with c, and why he uses lightening, light beams in clocks, etc in his examples. The reality of light has been equated with existential reality, and c is time.
Now, going back to my first, and obviously correct point, if one does this, then the omnipresent time delay, ie the real variable, gets switched from being the differential in the timing of receipt of the observable image, which it is, to a time differential in reality, which it is not. The reason there is, incorrectly, believed to be time in physical existence is, apart from a fundamental failure to understand physical existence properly, the attribution of duration to distance. This is effected when measuring distance in terms of the time incurred for something to travel along it, had it been able to do so, which it cannot, and then expressing distance in terms of elapsed time, which it is not. And guess what is used to do this? Yes, light.
So the whole argument is self-fulfilling, and wrong. A non-existent variable is introduced, and that is incorrectly rationalised by misappropriating a real variable. The elephant in the room is dimension alteration. That causes them to think that there is something different about relative motion, because the force which causes changing motion, ie a variance from the 'at rest' motion, also, supposedly, causes dimension alteration. Hence the aversion to non inertial frames (ie references) and the perceived need for a correction (aka transformation) to make them equivalent to an inertial frame. But in reality, what they are actually doing, because light and existence have been conflated, is compensating for the optical illusion I explained above. A sequence will appear to alter its rate of change (aka time) when relative spatial position is altering. However, if the original error is not understood, then this effect is misunderstood and is deemed to a feature of existence.
Using quotes from section 9 1916:
We start with: "In this manner a time-value is associated with every event which is essentially capable of observation." Which because timing devices allegedly act in a stange way, ie: "It has been assumed that all these clocks go at the same rate if they are of identical construction." Results in physical existence being depicted as being in what amounts to a state of anarchy: "Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event." Which leads to the incorrect assertion that: "Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity". That definition being wrong.
Paul