“I can’t think of a single mature company that has managed to change its culture.”
Much depends on how you define ‘culture’. I can think of a few long-running and successful companies which have, over years and sometimes decades, changed their reason for existing, which sponsored a change in culture.
Wells Fargo, for example, started as a delivery service, which has substantially different goals, incentives, and strengths than a bank. Sure, there are characteristics which serve both, like an emphasis on integrity and security. Are those (the dominant) cultural elements? Depends on one’s definition of culture.
But Wells is not a once-in-all-time example, either. Most U.S. airlines (well, the surviving few) come to mind, now selling seats rather than an experience. Give me some time and I’m sure I could come up with others.