There is a scale of how important an communication method is. At the top are emergency services, which can literally save lives.
Twitter and phones are both life-saving services when used for emergency services. Because of that, neither should be taken offline for any reason.
But Twitter has other important uses in the sharing of real-time information. Many real-time reporting services, such as crime, weather and traffic reporting, are built on it. For some people in some situations, removing Twitter could have a serious negative impact, even if not life-threatening.
So taking Twitter offline should not be compared with taking Wikipedia or Reddit offline, for example. While all three allow real-time changes, Twitter is heavily relied upon for real-time emergency services, Wikipedia and Reddit much, much less so.
Not even Wikipedia’s founder thinks Twitter should go offline:
