Twitter won't automagically stay online. A complex system needs dedicated and experienced engineers to maintain it, apply updates and troubleshoot issues, and that's if you're not actively developing new features.
So it will coast for a while before the wheels come off. Maybe performance will degrade, maybe media stops loading or your timeline won't refresh. Maybe none of that happens and a critical system deep down fails and it just stops. But Musk has all but ensured that Twitter in its current form cannot continue to function.
I strongly suspect that was a case of switching off something that few people realized was required by for MFA service to operate. That speaks to poor comms, poor docs, and poor understanding of the systems (by the people who were still around.) "Chesterton's Fence" says you shouldn't be turning off stuff you don't understand, but if it looked OK to turn it off, but it wasn't, then that's actually an indictment of the poor engineering practises that Elon claims are rampant around Twitter. Rather than showing Elon to be an idiot it might prove his point.
But we're not in Twitter, so we can't know. What I would say is that if everything was well signposted that the service was critical then I doubt Elon would have recklessly ordered it should be turned off regardless. He's not that bad. It smells of bad documentation to me.
In the hypothetical fantasy scenario in which I'm assuming leadership of a company that I claim is plagued by poor engineering practices -- practices which include bad documentation -- the last thing I would want to do is order people to turn off stuff without making sure that the stuff they're turning off is mission critical. Hell, I would do my best to make sure I don't issue orders that could even be misconstrued as that.
But hey, maybe that's why I'm just an engineer without any interest of making the switch to the "leadership" ladder, and not a CEO.