The existanceexistence of the speed limit is related to the existanceexistence of time [UPDATE: time is a measurement which is only available when $c$ is limited. If you aredo not agree, provide a way to measure time when $c$ is infinite before downvoting]down voting]. If there'd be no speed limit, everything would happen instantly. Also, any waves in any matter would not be affected and spread momentarily. Time would disappear (as well as distance and, consequently, space, btw).
So, it is the same as "why is there time?". Instant energy transfer which is currenlycurrently limited would change the world as we know it and it would not be this world that we know anymoreany more. The newtonianNewtonian physics would disappear as a concept, since the matter itself would not work like that anymoreany more. As well as the concept of form. The consequenciesconsequences would dawn on everything. However, we are not observing this, we observe the limit.
There is some inherent separation present in the Universal matter, which allows it to exist the way we know/perceive it. If there exists a world without the limit, we did not emerge in it, we appeared here.
Not exactly an answer, but there's nothing else to say
UPDATE
In response to Davors@Davors comment:
It is hard to picture what would exactly happen because we can't be sure what is the actual underlying structure of the reality that makes up for the speed of light and how is it intertwined with the rest of things. That is - how would the other 3 forces form the matter if EM was instant. But lets explore some options that support the notion:
There are 4 forces, and if the EM force would transfer all energy instantly, then even if the 3 other forces still would hold, it would invalidate most structures bigger than atoms of the matter we see now. Since on macro level only gravity and EM do matter, and gravity will have no big sense in this scenario, then all processes that are conducted via EM forces will be instant.
No macro structure could exist, and with all EM processes going infinitely fast, there would be no possibility to know anything about electron states in the atoms. They will become infinitely every possible states. All possible absorbtionabsorption and emission will happen at once. Not sure even if atoms would hold up.
Try putting infinity instead of $c$ in all the relations and see what happens. Also, as all speeds can effectively be measured as a fraction of $c$, then if $c = \infty$, all other speeds will also be infinite no matter the fraction coefficient.
See the reply by Nikos@Nikos M.