Two thoughts:
1) Sometimes a proper diagnosis can only be done by engaging -- attempting to learn more about the problem, what's most sensitive to a remedy working, etc. So 'aim carefully' isn't feasible here, because the target is moving, and fire-missed is actually crucial to figuring out the dimensions of the problem.

The 'aim carefully' is a matter of judgment and interpretation.

2) More often, I see the 'fire', 'missed it', 'aim quickly' 'fire again' as reflecting priorities or culture in a management system. Could be driven by timing of budgets being available, rewards for 'taking action' (regardless of results), or competition among leaders for scarce resources (get what you can when it's available).

Interesting, I see that businesses frequently reward inputs or self-measured (internal) outputs, rather than outcomes (which reflect the impact on others or markets/customers) -- actual value.

Is it because fire fighting still gets rewarded in organizations?

What happen to me is that sometime we are so in a rush trying to fix anything as soon as possible that we did not take the time to assess the situation in the right way. People sends email highlighting urgent any time with crazy loop of persons in cc, this just create more stress and increase the pressure with no helps. The main mistake is then trying to cater team expectations as soon as possible without taking your time, if you fail then have to start from the beginning and this will just cause more delays

There are different sides to your question as part is cultural determined and part is basic Effective Problem Solving.

Some cultures (corporate, regional, national) tend to focus on the last and visible cause and strongly focus on that part in the bigger picture to enforce managers' authority immediately and are sometimes also driven by revenge. An approach like that comes usually from a strong authoritarian approach. My experience with such an approach is that you run the risk of creating an atmosphere of fear and intiidation. Mistakes which creates problems are mostly caused my human errors and I do not believe these errors are caused deliberately in most cases. So by inimidation and punishing the person who made the mistake only grands you short term effect because the underlying cause is not looked into. Therefore the root cause might still be present and will cause similar problems eventually. Another consequence of this approach of immediate action and punishment based on a strong authoritarian approach is that things will escalate easily and might lead to time consuming and/or money consuming situations.

An effective way for dealing with problems is to focus on the root cause and learn from the conclusions. This is a long term strategy which will benefit the organisation, internal harmony and supplier relations (if suppliers are involved) much better. Another part is how to deal with person involved in causing the problem. If a serious midconduct, wilfull is even worse, a good conversation is needed on management level to discuss the role of that person in the problem. Create awareness instead of a fearfull worker. Let him be part of the escalation team responsible for dealing with the situation and problem solution.

Good discussion.
Shrikant, as your question correctly identifies - many people get into the trap of confusing decisiveness with problem solving. They have a ‘rush to solve’ bias and thus they rush to action and more often than not,  fail to define the real problem, and jump to conclusions.
Sir Richard Branson of Virgin Group has said “One vital component of decision-making that is often overlooked is quiet contemplation. After looking at all the stats, speaking to all the experts and analyzing all of the angles, then take some time to yourself to think things through clearly.”
My experience is that if we take the time to define a problem well, many a time - you make them easier to solve, which means ACTUALLY SAVING time, money and resources.
Especially leaders should stop trying to show or feeling the pressure to show that they have all the answers (i.e. be a hero). Unless it is an emergency where the team is looking to them to decide super-quickly, they should ENABLE THEIR TEAM by helping define targets, creating a safe environment for raising problems, ensuring people have enough time for problem solving, and helping them develop their skills. Over-confidence is a third reason why people shoot first even before taking aim.
A fourth reason - I'd attribute it perhaps to the wrong habits caused due to advances in technology. Am not blaming Tech itself. How easy and painless it is to "erase" or "recall" SOME mistakes (e.g. think back to mistakes you made when you only had the typewriter and not the computer; NOW even WhatsApp has introduced the message recall facility; )

To define a problem and identify root-cause, there is the famous "five why’s'' technique. I rely on the underlying principle emphasised in the approach - the truth is sometimes it takes only 1-2 whys. Other times, it may take much much more whys. The trick is to ask as many times as needed until we feel we have gotten to the source problem.
It is about solving the right problem and than means first identifying and defining the problem(s) at hand. Else it will be a case of ‘marry in haste and repent at leisure’.
However, in the same breath, I want to assert my conviction that there is little merit in waiting for the perfect information to decide because that is never going to happen. Once one has ~60-70% of the information needed ( this is a judgement call) and based thereon you have defined the probem and weighed factors carefully, you have got to go ahead and decide and then be willing to be nimble/agile and course-correct if needed. Hope am making sense.

I think this all comes from the psychology of the pressure. A lot of time managers/leaders think the pressure or quick responses will improve the productivity. However, it is the other way around. Sometimes it may work but this practice is dangerous to repeat again. They try to solve every situation like a crisis situation and hence routine problems become a crisis. 
I think in your suggestion - 
Ready - Aim Carefully - Check Again - Hit the Target
Ready and Aim Carefully is the part of an analysis of the problem. This is a must. And I have seen, if you work with the team in analyzing and aiming the problem, you save a lot of time in execution (i.e. Hit the Target).