There Weren’t That Many Flashlights
As soon as disaster takes its course, you can see multiple crew members searching the ship for survivors. They do so with flashlights in hand to illuminate the darkness, which would’ve made the search-and-rescue operations nearly impossible. While having a flashlight on hand for such emergency situations would make sense, it wouldn’t make sense at the time.
In 1912, the Titanic wasn’t equipped with a flashlight for ever crew member. This is because they weren’t mandated to prepare flashlights for emergencies (we’ve learned since then). In fact, the only people who actually had flashlights on hand were the forward-thinking passengers who packed them in their suitcases.