Can't talk about PA, but from personal experience the reason clients hire ACN is to get stuff done that their own people are too slow, inert, dumb, or incapable of doing.
To be corny about it, that's why there's the "Delivered" in the company's catch phrase.
(That's not to say they always "do" everything right, as evidenced by experiences at NHS, Centrica, RPA, etc. - but each of these cases will have a number of reasons for the screw-up).
Would be more accurate to say that the only thing that MBB consultants ever "do" is research, modelling, powerpoints, and presentations on findings and recommendations. They then leave the "doing" of the results (i.e. putting into practice, operationalising, implementing, executing, etc.) to someone else. Cue ACN.
Perhaps this is just another argument to call PA and ACN people something other than consultants...