I get your point but if you think that list of critical functions (or the unlisted "good ol boys" style tasks) boils down to some emails then I think you don't have an appreciation for the work or finesse or charisma required.
We could solve that by replacing all CEOs to remove the issue of finesse and charisma. LLMs can then discuss the actual proposals. (not entirely kidding)
It would be actually nicely self reinforcing and resisting a change back, because now it's in board's interest to use an LLM which cannot be smoothtalked into bad deals. Charisma becomes the negative signal and excludes more and more people.
Why are there "good ol boys" tasks in the first place? Instead, automate the C-suite with AI, get rid of these backroom dealings and exclusive private networks, and participate in a purer free market based on data. Isn't this what all the tech libertarians who are pushing AI are aiming for anyways? Complete automation of their workforces, free markets, etc etc? Makes more sense to cut the fat from the top first, as it's orders of magnitude larger than the fat on the bottom.
A more fair, less corrupt system/market sounds great! I also think once we solve that tiny problem that the "should ai do ceo jobs" problem is way easier!
What should we do while we wait for the good ol boys networks to dismantle themselves?
On a more serious note, the meritocracy, freedom, data, etc that big tech libertarians talk about seems to mostly be marketing. When we look at actions instead it's just more bog standard price fixing, insider deals, regulatory capture, bribes and other corruption with a little "create a fake government agency and gut the agencies investigating my companies" thrown in to keep things exciting.