Who knows what he needs to work on in his first 3 months? Perhaps it is important to listen and understand everything before making decisions, rather than jumping to react so it looks good from a PR perspective.
Writing any culture statement is not hard, but running a process to understand the organization, set a clear direction for the future, and then solidifying values so that everyone in the organization knows is not. Writing a culture statement is also not the only thing he's done, just something that is public.
On a side note, the second you say "lavishly paid CEOs" and "he gets paid enough", you bring a level of disdain into the conversation that makes it hard to continue. We should absolutely hold CEOs of large companies to a high standard, not because of their pay, but because of their position and the responsibility they hold.
Identifying and owning up to the 8 years of toxic behavior is hard. That’s what would stop the negative news cycle. It is definitely hard, but he gets paid enough for us to have high expectations.