My dad ran a crisis management consultancy for years. I just googled a few of his clients and they all survived the process. He would come in, assist with minor layoffs, repair business processes, usually get some software installed/updated back when that was a huge multiplier to a business and then leave when everything was running smooth.

I also am aware of a situation where a pair of business consultants who were meant to be assisting with a software project were diverted (at full rate 1200/day) to assisting with redecorating an office.

I was directly involved, oppositionally, to a pair of business analyst consultants who tried to get a customer of mine to change their (admittedly terrible) vendor selection by repeating security concerns over and over again in the meeting. They never actually got to the point of analysing said terrible vendors terrible integration practices or costing up a migration path. They just banged on about security and contacted us separately after the meeting asking for more details about the security situation.

Basically you get out of it, what you want to get out of it. It depends on the consultant, their education, and the terms of their engagement. I don't know if statistics would be useful in this scenario or how you would control for wildly different outcomes.