Would PreCrime really collapse in reality after the events in this film?

A lot has happened in the real world since this movie and the mentality of today's society makes me very sceptical that the public "oops" at the end of the film would be enough to make people lose faith in the system to the point it's abandoned.

One thing is the large support of capital punishment. Plenty of "minority reports" are made public. Innocents do get executed. Studies have shown that capital punishment doesn't even lower crime rates, so there is not even an increase of national security. People find the payback-principle of it somehow worth the risk of executing innocents.

Then there is the public attitude towards security. In Minority Report, it's extremely clear how PreCrime actually does prevent crime to an immensely succesful degree. Murders do not occur at all in years.
In reality, people are willing to risk their lives and that of others in large scale warfare, because it's said to sort of protect national security. No one really knows to what extend. It's really vague and hard to measure.

All this shows how high a price people are willing to pay for even the slightest possibility of increased security. I also have the feeling security is kind of an addiction. As seen in the film, after many years without murder, it's exceptionally shocking when it happens again.

So in a system where very sporadically an innocent gets halo'd, just three people are used as lab rats, but zero homicides as a crystal clear direct result of said system... wouldn't most people be very willing to turn a blind eye and always ready excuse such minor "slips"?