Question

As the moon visits are still controversial to some people, why does NASA not use the Hubble Space Telescope to show images of the landing sites?

Answer 1

See below.

Explanation:

This has to do more with the human nature, as it is hard for someone to change their beliefs on something quickly - whether it's the moon landing/moon visits to facts about a presidential campaign to whether the Earth is flat or not.

There will always be skeptics, facts shown will be declared as "false" or "made up" to preserve the idea that the person was right all along. This article by The New Yorker has a line from it that I think sums it up perfectly:

"Consider what’s become known as “confirmation bias,” the tendency people have to embrace information that supports their beliefs and reject information that contradicts them."

Another article by Scientific American also states:

"These experiments show that when people's beliefs are threatened, they often take flight to a land where facts do not matter. In scientific terms, their beliefs become less “falsifiable” because they can no longer be tested scientifically for verification or refutation."

So basically, even though some might change their minds after seeing the images from the Hubble Space Telescope, it is not guaranteed to work. Unfortunately it is not as simple as showing someone an image to change their mind, but it may help.