I'd guesstimate that Twitter probably has dozens of services that are in the critical path of an average user interaction. It's hard to keep even logically optional dependencies truly optional in large scale systems involving many people.

However Twitter didn't die in the past when fail whales ruled its day, so they probably won't kill it now. It's just not that kind of business. (In contrast, a one hour outage had me directly apologizing to our largest customers on the phone). That said, Twitter can only be unstable and lack feature growth for so long before something else takes its place, so Musk is on a clock.