Poynting-flux and magnetic charges

in the derivation of the Poynting-theorem one needs to substitute a term \(\vec{B}\mathrm{div}\vec{B}\), which is equal to zero due to the fact that the magnetic field is purely rotational, \(\mathrm{div}\vec{B} = 0\). insisting to introduce magnetic charges by requiring \(\mathrm{div}\vec{B} = 4\pi\rho_\mathrm{mag}\), would that lead to a violation of energy-momentum conservation? are there other arguments, e.g. from the covariance of electrodynamics, why this is not possible?