Everything Lost at Alexandria was Already Lost

 The most basic form of security, which everyone thinks of, is to have two copies. If there was already only one copy, and it was at Alexandria when the library burnt, it means it was already the case that nobody cared to preserve it. If it hadn't been lost in a fire it would have been lost less dramatically, that's all. 

 Even at its height Alexandria wasn't, like, good. It was apparently in the main a collection of poems and scholars of poetry. Nice and all, but not the height of intellectual inquiry here. The loss of Alexandria was like losing all the sole copies of a bunch of web novels.

 

 Further, the legend of the fire seems to have been dramatically overblown. Hollywoodized. Turns out librarians are aware that fire is a hazard, and the fire was put out using the established anti-fire security. Whoops. Nothing was lost when it burnt, and also it didn't actually burn.
 Shockingly the library was run by men, whose reaction and response to events will tend to action and mitigation. It wasn't run by women, who react to events by emoting and talking about these emotional responses. Today "react" and "respond" largely refer to posting about it. Tweeting doesn't extinguish fires, not even at e.g. the Notre Dame, fun fact...

 When the library was for certain destroyed around 270 AD, it was already several centuries past relevance. It was primarily razed by lack of funding. It was not secured because there was already nothing left to secure.  Because demand for scholarship, even easy cut-rate scholarship, had already vanished.

 Women didn't run the library when it was burned in a civil war, as this was BC. A daughter library remained many centuries later, but was ordered demolished by a Christian bishop. What a coincidence.