Worrying takes up too much effort and removes the ability to work effectively on solutions to problems and ways of mitigating the risk of those problems arising again. Also, in a team environment, being that guy/girl who keeps one's head, focuses on the problem and begins the process of moving forward to a resolution can be good for one's future in the work place. I like being that dependable guy, it's good for my sense of value and worth (personally) and has also helped me progress through (upwards) within the organisations I've worked with.
There's also much to gain personally from having this ethos and the work don't worry phrase can apply to, and be of so much benefit in, most people's lives. It's not all that hard either...ok, it can be, but generally it just requires a little discipline to get started.