Why can't the conjugate base of benzoic acid be stabilized by conjugation with the aromatic ring?
Here are some of the resonance structures we can draw for the carboxylate anion of benzoic acid.



You're correct that we can't delocalize the negative charge from the oxygen into the benzene ring.  Even though there is continuous p-orbital overlap between the oxygen and benzene carbons, there is just no way to push the electrons so that a negative charge winds up in the benzene ring. However, as the resonance structures show, we can move electrons the other way and place a second negative charge on the oxygens and leave a positive charge delocalized around the ortho and para positions in the benzene ring.  This is why the carboxylate anion of benzoic acid will not react with electrophiles (electrophilic aromatic substitution) at those positions in the aromatic ring.