If all your energies are dedicated to just completing a task, you will almost always decide to do it a way you know for sure will work. To innovate; to find better, simpler, faster, or more elegant solutions, one needs to have time to think about the problem at hand. Innovation needs you to experiment, have time to make mistakes and recover from them.
Naturally no one has infinite time to solve a problem. But if you are very hard pressed for time, processes will stagnate. Innovation will almost come to a stop. I believe that one should always be pursue innovation. That means that one should always have more time alloted for a task than strictly necessary.
The road to innovation is not by thinking out the best way. But by experimenting on several alternatives. Making the mistakes along the way. And learning the lessons forever.
Keep experimenting. Keep innovating.