Maybe they would, but then that’s part of the problem. If representative government has any value, it’s not in amplifying the impulses of people in the confused heat of the moment, but in standing for what they would still respect the next day.
Pericles watches the Spartans burn the countryside, tells his furious electorate he will let them instead of being provoked into a rash defeat, and is the better for it. Bush reacts to 9/11 with fury and leads his country into a broader disaster, one that has helped the rise of groups like ISIS. You can call that human or what his countrymen wanted, but there was no shortage of humans sober enough to protest it.
There is a trick here, that because such attacks are spectacular people forget what risks they really face. I don’t think you calling safety a fundamental need is wrong; I’ve argued before that security vs. liberty is a false choice and each needs the other. But that just makes it worse to shred actual safety for momentary illusions, exacerbating the problems that promote terrorism in the first place.