Improving the system effectively demonstrates a high level of skill. This should be recognised and rewarded.
What are you rewarding
Effectively improving a system requires three elements to be in place: 1) Actual working knowledge of the present system, how it works and what it does, 2) Insights into where the system falls short or could be optimized and 3) An effective development and implementation of the improvement, making sure the system actually improves instead of accidentally getting worse.
People who quickly (and sometimes constantly) claim that "the system does not work and they know better" often have not really tried to work with the present system, and mistake their lack of experience or skill with faults in the system (a good example of the ego-trap). When somebody really improves the system, you are rewarding not just the improvement, but are actually rewarding the three skills mentioned above: Good knowledge of the present system, good insights into possibilities for improvement and a good and safe execution of the change.
How you are rewarding
Make sure that you reward "improving the system" as being the norm, rather than the exception. If you make it too special, a majority of people will think "Ah well, this is not for me" whilst in reality this is what you want: Continuous, well considered improvements.
So, reward this behaviour actively on the workfloor. Compliment people, support people who come with improvements, take them seriously if they come with serious ideas (which by the way can also sometimes seem silly in the first instance). Reward it with recognition, appreciation, resources and attention from management. See if you can give it a place in your career-development program.
By rewarding this behavior you are contributing to a good safety culture by teaching the whole team to really value good application and constant critial evaluation of current working practices, and by teaching the people to contribute to creating a system that works as the safe haven that prevents errors and damages. And you wished more teams were working like that! By the book, helping each other out, and intervening at the right times.
If the team consistently demonstrated good performance, consider rewarding the leader or manager by recognizing how he or she has built an environment and skills in which a team can succesfully improve.
And, as always, avoid the ego-trap and protect people against this. We improve as a team and for the team and you are recognized because you contribute to the team, not to your own ego.