> Why would we ever think that the time interval between two events can depend on the reference frame?
This isn't a postulate, it's a derived theorem. That's true no matter what axiomatic formulation you use.
> All the individual phenomena (time dilation, length contraction, relativity of simultaneity, constant speed of light etc.) are very hard to understand, because you cannot just take one of them and add it to classical relativity without immediately running into paradoxes. Only once the whole picture is known you see that all the pieces beautifully imply each other.
This is all true, but all of these things you talk about (except the speed of light) are not postulates; they are derived theorems. No approach to relativity that I'm aware of has ever tried to start with any of these things as postulates. Even Einstein's original 1905 paper didn't start with any of these things as assumptions. He started with the principle of relativity and the speed of light being invariant. This paper is just showing how to derive at least a part of the second assumption from the first.
"Let us consider two events, E1 and E2, at the same spatial location in frame O, but separated by a time difference τ. In O′ the two events are separated by a time lapse T."
If you didn't know special relativity, you would never get this idea.
> If you didn't know special relativity, you would never get this idea.
You're looking at it backwards. The paper is not assuming anything here; in fact it is explicitly refusing to assume that we know the correct transformation law between frames. That means we have to leave open the possibility of the time difference changing, not because we know SR, but because we are being logically rigorous.
This isn't a postulate, it's a derived theorem. That's true no matter what axiomatic formulation you use.
> All the individual phenomena (time dilation, length contraction, relativity of simultaneity, constant speed of light etc.) are very hard to understand, because you cannot just take one of them and add it to classical relativity without immediately running into paradoxes. Only once the whole picture is known you see that all the pieces beautifully imply each other.
This is all true, but all of these things you talk about (except the speed of light) are not postulates; they are derived theorems. No approach to relativity that I'm aware of has ever tried to start with any of these things as postulates. Even Einstein's original 1905 paper didn't start with any of these things as assumptions. He started with the principle of relativity and the speed of light being invariant. This paper is just showing how to derive at least a part of the second assumption from the first.