I heard once that smoke detectors save thousands of lives by waking people during a fire, but that thousands more are killed and hundreds of thousands are injured by falling off stepstools and ladders while trying to test or change the battery.
Also, what you want to compare is the number of deaths caused by falls from falling off the ladder when changing smoke detector batteries and the number of deaths prevented by the presence of smoke detectors.
Yes. We don’t know how many deaths were prevented. But if chance of death from falling from ladder when changing batteries is significantly smaller than chance of death from smoke, fire and flames, then it’s worth to risk changing batteries after all.
Unless you are elderly, especially above 85. They have much higher chances of dying from fall. Ask your younger acquittance or family member to change that batteries for you.