Why don't they try to change the past?

Caveat: Looking for logic in time-travel movies is an exercise in recursive futility.

The idea in 12 Monkeys is that the past is, in many ways, read only. You can go back and "read" all you want, but you won't be able to "write" anything that will (meaningfully) change the timeline. Alternatively, you can attempt to change an event, but since the timeline is already set, it accounts for your "hack" and adjusts events to reconcile the "new" timeline to the original version.

Keeping the above in mind, the scientists in the future are content to send people into the past to get information and communicate it back to them in the future. The scientists are aware of the paradox that if they could change such a catastrophic event in the past, then they wouldn't be considering doing so at all (in their present). Presumably they have tried to change things in the past and know that it's something impossible to do. They are, therefore, happy to use time travel purely as an archaeological avenue to find out enough information about the virus to allow them to synthesise a cure in their present.

This subject is tackled to an extent in an IMDb FAQ:

Why can't the future be changed, as Cole says?

There are roughly two major schools of thought on the subject of time travel in (science) fiction. One is that a timeline is 'flexible' and can be changed. When a certain outcome is undesireable, one needs to travel back to a point in the past, and change whatever caused the undesiarable outcome to happen. For instance, in order to save your mother from being run over by a car, you travel back in time so that you can push her out of the car's way and save her life. Most popular movies about time-travel adhere to this principle (e.g. Back to the Future (1985), Donnie Darko (2001), The Terminator (1984), and The Butterfly Effect) (2004).

Another theory is that the timeline is 'fixed' and can't be changed. The present is already the result of the past plus all attempts to try and manipulate the present. This implies that whatever you try to prevent by traveling back in time will be unsuccesful, or, worse, instrumental in causing whatever you tried to prevent. In case of the mother example, according to this theory, you can travel back in time to a moment before she was hit, but any action you might take will not be succesful in saving her. Possible scenarios are that you don't make it in time for some reason: perhaps in your hurry, you are hit by a car yourself, or you could shout at her to watch out for the car, thereby distracting her from the traffic, and thus causing her death. Movies following this principle are Sphere (1998), Harry Potter and the Prisoner of Azkaban (2004), The Time Machine (1960), and Twelve Monkeys.

Cole says that the future can't be changed, which proves to be true. Throughout the movie we see and hear about things that are said to happen in the future, and they all inevitably happen. Of course, the main event is that the global virus infection occurs. Cole's mission is not to prevent it, because the scientists know he can't; the very fact that the infection happened is evidence that it could not be prevented anyway. Furthermore, by traveling back into the past, Cole sets in motion a chain of events that lead to the very future he comes from, e.g. the mysterious recording by Kathryn to the future, in which she identifies the Army of the Twelve Monkeys as the source of the virus. Cole and the scientists hear the recording and Cole is sent back in time to investigate; however, because of Cole's interactions with Kathryn Railly, he causes Kathryn to make this recording. In essence, the events that trigger him to travel through time actaully cause them, which is known as a time paradox.

The fact that the future is set does not prevent Cole from trying to change it anyway. It is in his nature to try, simply because he does not know the exact details of what caused that particular future to happen and what his failure in trying was. For instance, it is known in the future that there was an outbreak of a virus, but not who or what started it. After the Army of the Twelve Monkeys appeared to be a dead end, Cole and Kathryn identify the real perpetrator at the airport, and try to stop him. This ends in Cole's death, which is witnessed by the young Cole, explaining the strange dreams he always had. It had never occurred to the young Cole that he actually saw himself dying, so the adult Cole never knew what fate would await him if he would try to prevent the virus outbreak.

There are two approaches to time travel science fiction:

1. That time is ONE fabric and continuous. Which makes it sort of a physics law that the past cannot be changed.
2. Time is something like a dimension. Which means that there can be alternate realities, parallel realities, well take your pick.

In 12 Monkeys, no matter what the actions are, the consequences are always the same. E.g. Red Army herring, Releasing the virus, Cole appearing in various books. So it is more like the first time function. Cole may go in his past, but in no way shall his actions change the present. What that can be interpreted as is that what has happened, will happen. No matter what actions you might try to take to prevent it. His being shot in front of his younger self is explainable as it is something the adult Cole has lived with his entire life. He remembers the Woman's eyes in his adulthood even though he was a kid and saw her just once. Thus, these events has already happened in Cole's past. And hence, it was impossible to change that past. This is also why Cole was sent on a recon mission, to observe and to report.

Also, I would like to point out to you that Cole was given the gun at the airport. At that point of time, Cole had defected and could not be contacted. So why did they give him a gun? They had other people in the past who could have stopped the guy just as well... Just a point to ponder upon. Had Cole not tried to shoot the guy, would his younger self have seen the shooting and the Young Woman? That's the time-paradox, which cannot happen at all in such time lines. Hence the linear consequence of the timeline and the unchanging past.

From what I gathered:

Our protagonist was unable to change the past because it was part of his present. He could have changed everything had he been told by someone else sent to him. This person would have to have gone to a timeline where the same big event ocurs, found out the truth and then go back to our progagonists timeline to let him know

The people in charge could have changed things (I think) but didn't as it's likely they wouldn't be in charge in the altered reality. They were in a position of power that was too beneficial to them to care about everyone else.

Physicists who research the theory of time-travel generally conclude that only two results are physically possible: (a) A single fixed timeline [already discussed]; (b) A variant of Everett's Many-Worlds Interpretation of Quantum Mechanics - in this case changing the past means creating an independent alternate timeline.

If arrival of the time-traveller ALWAYS creates an alternate timeline (with him/her on that timeline), time-travel would be useless to the senders [it would be like disintegrating the traveller]. But it need not do so: If each choice made by the time-traveller leads to a different timeline for each outcome, maybe one outcome stays on the original timeline.

I.e we could end up with an original timeline of type (a) combined with multiple alternate timelines branching off at various points in history following the arrival of the time-traveller. Note that this is the only way the time-traveller can stay on the original timeline and so be able to return to his/her original time - there is no 'cross-talk' between timelines.

BUT NOTE: For the ones who sent the time-traveller, EITHER (a) or (b) looks like (a). If 'changing the past' means 'creating an alternate timeline', then 'changing the past' is useless to them.

As I think no answer is right on the spot I will answer my own question with big thanks to the others from where I got the useful info to do so:

Answer: it is a law of nature

From: http://www.imdb.com/title/tt0114746/faq?ref_=tt_faq_1#.2.1.8

A "theory is that the timeline is 'fixed' and can't be changed. The present is already the result of the past plus all attempts to try and manipulate the present. This implies that whatever you try to prevent by traveling back in time will be unsuccesful, or, worse, instrumental in causing whatever you tried to prevent. [...] Movies following this principle are Sphere (1998), Harry Potter and the Prisoner of Azkaban (2004), The Time Machine (1960), and Twelve Monkeys."