Does Friedel-Crafts reaction fail with benzoic acid? I know that Friedel-Crafts reaction  (either alkylation or acylation) fails with phenol and aniline, due to formation of a coordinate bond between Lewis acid catalyst and the lone pair of the respective functional group.

But I have read that even benzoic acid fails to undergo this reaction. I couldn't think of a reason for this. Can anyone explain why is it so?
It could be that $\ce{-COOH}$ group is electron withdrawing hence there is an increased electron density in $\ce{-COOH}$ group due to -R resonating effect of electron from benzene ring.

Since friedel craft catalyst is a Lewis acid (electron deficient) the catalyst (anhydrous $\ce{AlCl3}$) reacts with electron rich COOH group of benzoic acid and gets bonded.