If you ask most people whether they support having a universal DNA database, they will say “no,” even though such a system is likely to reduce crime. People rarely judge hypothetical government policies on the basis of utilitarianism, and they often have a strong bias toward the status quo. Yet I think that if a universal DNA database were to be implemented, it would eventually gain broad support. We accept all sorts of government programs that violate greater freedoms for lesser results. Any attempts to repeal this program would likely be met with scorn.
Now, why do I think this? Well, if you'd asked people ten years ago if people should be forced to wear masks or social distance in the event of a global pandemic with a relatively low death rate, I think that almost everyone would say no. Similarly, if you'd asked most people 400 years ago if the US government should implement the amount of taxation we have today, most of them would oppose it. When asked about a hypothetical government policy, almost everyone seems to think that the ends don't justify the means.
Take the nuking of Hiroshima and Nagasaki as an example. If such a decision were being considered today, it would be extremely controversial, even if it was guaranteed to prevent a greater loss of life later on. People would be horrified at the prospect of killing hundreds of thousands of innocent people. Yet when these actions are judged retroactively, I've never heard anyone on either side advocate for a moral framework other than utilitarianism. Even those opposed to the bombings argue that they were unnecessary, not that killing some people to save a greater number is unjustified. Everyone seems to agree that if the bombings of these two cities was necessary to prevent a greater loss of life, then they were justified. Similarly, a draft order today would be very controversial, but no one seems to oppose the Civil War conscription order or any draft order that was historically successful in helping achieve some desirable outcome.
You've probably heard the phrase “Nothing is as permanent as a temporary government program.” Once high taxes and social distancing policies were implemented, no one was willing to accept the costs of removing these programs. It would likely be the same with any other sort of program that achieved a net benefit, so long as the benefits were very easy to observe.
So which standard should we use? Do the ends justify the means? I'm not sure that they always do or always don't, but I find it interesting that people judge policies retroactively by a different standard than they judge policy proposals.