Time is a dimension, but not like space

Also consider the speed of light is also the speed of causality. If there was no such limit it means it would be possible for effects to precede causes which would lead to a very different kind of universe!

How could an effect precede a cause if there were no speed limit to causality?

No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).

Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.

Here's a great video explaining how, due to relativity, FTL travel can cause grandfather paradoxes: https://youtu.be/an0M-wcHw5A?si=RYFGOmQOlaC2t0bM

Edit: in short, not all reference frames can agree on the order of events, and FTL events propogate "backwards" between some reference frames.

That doesn't mean that light (causality) couldn't be faster, right? You could increase the speed of light (causality) as much as you want and wouldn't run into any paradox.