The tensor density is not "artificially introduced". The numerical values of the four components of Ad are exactly the same as those which appear three times each among the components of Aa b c along with three each which are their negatives and forty zeros. So this is merely selecting a subset of components which represent the independent information in the original A.
If someone naively attempted to use Maxwell's equations in a curvilinear coordinate system or in the presence of significant amounts of gravity, then he would find that they still work in that context (except for the constitutive equations which relate D to E and H to B). How can this be explained in your ideology? It only makes sense when one realizes that some of the quantities are tensor densities.
So please see that I am not adding tensor densities to make life harder. Rather I am finding that they already exist and permitting their use to avoid the extra and unnecessary work of converting everything to ordinary tensors. Why multiply by the metric when you do not have to? Why use the Levi-Civita connection when partial derivatives will suffice?