Ex Director at a Big 4 consultancy here...
While I've done more than enough Powerpoint presentations telling clients what they already knew but didn't want to say out loud, there are some circumstances where bringing in a consultancy is a very good option.
Some examples:
As a software/cloud/data/AI/cyber guy (I wore a few different hats over the years...), I regularly caught up with buddies working in legal, tax, audit, retail, space travel(!!) etc. for coffee chats. It's surprising how often those of us who specialise in one domain had breakthrough moments from offhand chats with specialists in other domains. Very few people get the opportunity to have these sorts of conversations, and it's amazing how often you learn something relevant for your own work situation over a quick coffee.
When I needed expertise in one of those domains into one of my projects, I could send a message and almost always get someone on a call within a few hours. Very few organisations could get e.g. a high-ranking ex-NASA official on a call quickly to pick their brains, but I could.
Lots of times organisations don't have the deep expertise and/or available people to deliver on their internal projects. When a major rail transport provider needs to work out how to going to deal with new government critical infrastructure regulations for their IT systems, it's consultancies who can pull all the right skills together to help them out.
When there's a critical shortage of available IT skills in the marketplace, companies use consultancies to top up their workforce. Here in Australia, there were nowhere near enough GCP experts to go around for the last 4-5 years, so companies could either try to hire the very few people around at exorbitant rates, or tap a consultancy for resources.
Big 4 consultancies in particular throw high-quality training at their technical staff like nowhere else I've seen. One reason: quality training = billable hours. I had people around me burn out from too much training, and I'm pretty sure regular companies don't have that problem. For all the pointless Powerpoint presentations we did, there's a sh1tload of technical expertise sitting in Big 4 consultancies, waiting to be tapped.
Companies are always struggling with how to use the latest IT shiny tools properly. Right now it's AI - how can I use it to save costs or increase productivity? What are the ethical and legal implications that come with AI, and how can we deal with them? How can we deploy AI solutions securely? Which of our business problems are the best fit for AI solutions? How do we train our ops staff to keep these AI solutions running? - the list goes on and on.
Now a lot of people here in HN know how to do these things, but how does a regular business tap into that expertise and filter out the bullshitters? The answer is they go to a consultancy that (they feel) they can hold accountable.
On that point, sometimes execs in a company simply need someone to shield them from blame for unpopular decisions like mass layoffs. It's pretty well know that consultancies do a lot of that type of work, and they (justifiably or otherwise) cop a lot of crap over it so some exec can say "I didn't do it".
I'm probably coming across as a huge fanboy of consultancies, but remember - I'm an ex Big 4 guy. I think their influence is too large, particularly in government policy making; I've encountered way more sociopaths in Big 4 leadership roles for it to be down to chance; by any measure staff turnover and burn out is very high, and I'm convinced that's by design.
However, they have their place.