This negative charge on the carboxylate oxygen is 2 single bonds away from the benzene ring. But conjugation ALWAYS occurs when they are separated by one single bond.
Your structure is like -C=C-C-O-
Had it been -C=C-O-, then the negative charge could have stepped down from the O atom the double bond could have migrated(cleaved) to form a negative charge on the left C atom.
But this is not the case with our benzoic acid.