Chemistry: A Chemical Dilemma
You have it a little backwards.  We don't observe charge, and then infer the existence of a force.  It's the other way around.  We observe forces between objects -- they repel or attract each other -- and then build models which explain which objects are attracted or repelled by which other objects, and by how much.  That leads us to invent the idea of charge and assign it to objects, and later still to connect charge to other properties of the objects.

If your question is why is there an electromagnetic force at all, the answer is probably that it is easier to imagine a universe in which there are forces between degrees of freedom than one in which there are not.  Our current understanding of the universe is that can best be described as a set of fields, like the surface of the sea, and everything we see is some kind of ripple or wave in that field.  It's easy to see why ripples on the surface of the ocean should interact with each other -- exert "forces" of some kind on each other -- and hard to see how they could just totally ignore each other.  That's how it is with nature.

Granted, it looks like there exist wholly separate bodies (particles, objects, things) and we wonder why they should interact with similar things far away.  But that may be because our perception is severely limited, and the underlying fields are much more complex than the surface of an ocean.  If you want to explore the topic further, start by googling "wave-particle duality in quantum mechanics."