This utilitarian argument assumes that each life is of equal moral worth to save. Suppose that the three lives you would save are of convicted criminals, and the life you would have to take is of a newborn baby.
All of humanity's greatest achievements (visiting the moon, halving world poverty rates, drastically reducing inter-state wars, vaccines, improved standards of living, etc.) happened after Capitalism supplanted monarchical feudalism and merchantilism as the primary economic system.
True private property did not exist until property rights were respected, which is only around the time of the Magna Carta for Western civilization. Until then the king, lords, or bandits could come and steal your stuff without repercussion.