1) Enrich their partners
2) Lend credibility to their clients
Consulting firms are hired based on an "appeal to authority" fallacy. Companies don't want to make hard/unpopular decisions, so they outsource them to consultants. Data point: management consulting is one of the industries that is hit hardest by a recession. [0] If consultants truly provided value, this is exactly when they would be most needed.
The people actually doing the work on these deals are 22-25 year olds. They are highly incentivized to make their firm look good (thus enriching the firm's partners). Anything else is gravy. Anecdotally, I have many friends who worked in the industry, and when asked if they would hire consultants for their own hypothetical businesses, the answer was always "No".
I highly recommend this article on McKinsey's work restructuring Puerto Rico's debt - it pulls back the curtain on the industry: http://nymag.com/intelligencer/2019/04/mckinsey-in-puerto-ri...
[0] https://www.ft.com/content/1a229d54-4548-11de-b6c8-00144feab...