Monopoles are already accounted for though, because they’re explicitly ruled out by the character and form of the laws of electromagnetism. ∇⋅B = 0, or “the divergence of the magnetic field is zero”.
When Maxwell first published his work with the equations, it contained non-zero B divergence. We say that density of magnetic monopole (which should be there instead of zero) is zero because we did not find any monopoles yet (maybe ever!). If we discover a monopole, and we remove this zero, there will no problems with EM theory, and actually we can explain some other things like quantization of electric charge (why all charge are integer multiple of electron charge).
So no, it was not explicitly ruled out by Maxwell's equations. It is not even ruled out because we did not explore the full phase space. And it depends on which monopole you are talking about (Dirac monopole, GUT monopole or EW monopole).
I mean I we found a magnetic monopole then we'd just change that one of Maxwell's equations so it looks like the corresponding electrical equation Div(E) = ρ/ε. It essentially just happens that the thing which correspond to ρ for the B field is 0.
Except that if the divergence of the magnetic field were anything other than zero, the laws as presently written wouldn’t successfully predict electromagnetic effects. Because the laws as currently written _do_ make predictions, and exquisitely precise predictions at that, the divergence must be zero with no monopoles at all or so close to zero that monopoles would be extraordinarily weak if they did exist. Their effects would be so slight that they would be useless for any practical purpose except possibly impressing the Nobel committee.
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.
I don't really understand your point here. If we do discover magnetic monopoles (which would not necessarily be very weak but instead very rare) then we would take the equation
Div(B) = 0
And update it to say
Div(B) = sigma
Where sigma is a field describing the monopole density. Theres a ready "gap" in Gauss' law for magnetism where you can easily stick monopoles. Of course the divergence would be zero in the absence of monopoles, just as the divergence of the electric field is zero in the absence of electric monopoles, but decidedly non-zero when there's an electron around.
I think your point is the current Maxwell equations explain physics so well that if we change them to accommodate magnetic monopoles they would have to be worse. If I understand you right, it overlooks that we can add terms[0] to Maxwell's equations that don't affect predictions in a world free of magnetic monopoles:
∇⋅E = ρ(electric) / ϵ0
∇⋅B = μ0 * ρ(magnetic)
∇⨯E = -μ0 * J(magnetic) - ∂B/∂t
∇⨯B = μ0 * J(electric) + (μ0)(ϵ0)(∂E/∂t)
We could switch every physics textbook to using the above today, and the only difference would be setting ρ(magnetic) and J(magnetic) to zero when there are no monopoles in the problem.
[0] Griffiths Introduction to Electrodynamics 3E, Section 7.3.4
If anything it's frustrating that there aren't monopoles, because if there were, we could make the E and B equations symmetrical under interchange of the fields. It would be a lot prettier, and I think it would be easier to teach to undergrads.
I mean you could just do that and tell the students that the magnetic charge and current densities are always zero unless we eventually discover monopoles.
This is incorrect, you can put non-zero divergence of magnetic field and all the equations and predictions stays the same. Better it would make Maxwell's equations symmetric under exchange of fields and sources. \
> so close to zero that monopoles would be extraordinarily weak if they did exist
Why? I can't think of a reason why would this be the case? You are not solving Maxwell's equation for the universe. You can have divergence of electric field closed to zero because you have very low density (the field source) in the region you are studying.