[rnhmjoj]

The fact that standard EM theory with zero magnetic charge works well only proves that normally there aren't lots of magnetic monopoles floating around: they could be very short-lived particles or strange phase of the matter, but still real and Maxwell's equations don't say anything about this.

As far as I know there's no mathematical or physical reason to outright forbid magnetic monopoles. On the contrary, there is a well-known argument by Dirac that says that if they would exist then charge is quantised, which we know it is. This is one of the reasons people are still looking for magnetic monopoles.