If a user at a bank tries to transfer $10,000, gets an internal server error and retries because their balance hasn't updated (banks don't process these in realtime), and checks the next day and finds $20,000 gone, that's a big problem. The user can't be responsible for this, you need something more.
You're not wrong that this isn't necessary in the majority of cases (updating your email address?) - but the majority of cases don't need distributed systems. By the time you're talking about distributed systems (which is the focus of this article and discussion), you absolutely do need this, in the vast majority of cases.