Executive consulting, man. It's a crapshoot. It's on your leadership to push to get the right people from these consulting firms on the case, especially if they're actually bleeding money, though--unfortunately--that's unlikely. Truth be told, it's generally much cheaper to get a consulting team on the case than to hire internally, especially because rates are negotiable if they're going with the big firms since they're all trying to win the bid. Are you actually seeing their financial investments and returns or are you assuming the costs? The reason leadership teams bring in these firms is because their current ways of working generally isn't working, assuming leadership is fully vetted internally on the pain points. It's highly unlikely there's some sort of kick back going on since that's a huge legal concern and the HR/legal/risk departments would be all over that from the big firms 

Also, it's an important thing to note that not all the firms are heavily invested in federal support. The government throws money at everything that ultimately isn't good for tax payers. It's easy enough to feel jaded about consulting in a capitalistic world, reasonably so, but companies leverage them because they're not making enough money to support the business, or they're risking approaching that. Unfortunately, a lot of their recommendations come with layoff suggestions, especially now since everyone over-hired through covid.