In all the above discussion all the effects would go away is the speed of light were infinite. If there is a top speed, which by definition has and absolute value (the same for all observers), then all the above effects return. It is because the equations found by Maxwell involve an absolute speed, and because they agree with experiment, and because nothing has been found to travel faster than light in vacuum, and because all the consequences of the Principle of Relativity are verified again and again with the top speed equal to c, that we believe this top speed to be precisely c.
Imagine, as Einstein did when a teenager, what would happen is you could move at the speed of light. As you go by a village (for example) you'd move at the same speed as all the light coming form that village. So, if you look around, you would see the same things all the time, nothing would ever change since you are riding along with a single image: the one carried by the light from the village at the time you passed it. In your frame of reference time would stand still! (we will see, however, that it is impossible for something having mass --such as you-- to move at the speed of light. You can reach speeds very close to c but never reach the speed of light itself).
Imagine now what would happen if, for example, a rat manages to travel at a speed greater than c. Let's imagine that as the rat travels by you, you send a short laser light pulse after it. According to you the rat will gain on the light pulse steadily. Since the distance between the rat's tail and the front edge of the pulse increases the rat would think that the pulse is moving in the opposite direction. So you and the rat would disagree even on the direction along which the light is traveling. This, of course, contradicts the Principle of Relativity and/or Maxwell's equations and it shows that the Principle of Relativity together with Maxwells' equations imply that nothing can move faster than light.
This is a good feature: if a faster-than-light-rat could be found, the vermin farme of reference would have time flowing backwards. To see this imagine the rat going by the same village mentioned above. Since the rat moves faster than light it will steadily gain on the light beams than come from the village. As it looks around the rat will see the church clock strike 12, and, as it gains on some earlier images, the rat would wee the clock strike 11, etc. So events whose time orderings wer aboslute would no longer occur in the correct order in this frame.