The product behind the prestige
Formally, a strategy firm sells analysis and recommendation. What most buyers are also purchasing is assurance: a name the board recognises, a method that lends the answer authority, and cover if the answer proves wrong. There is nothing shameful in buying assurance, but it should be bought knowingly, because it is the most expensive component and the one least connected to whether the strategy works. The working component is the team's judgement, and that depends almost entirely on who is staffed and how much partner time your problem genuinely receives.