There is little use in being able to integrate functions, or to solve trigonometric equations, or to rearrange equations. However, being able to do these sorts of things without thinking too hard then releases the mind to think about other things with freedom.

Similarly, effortless recall of the pros and cons of different algorithms and data-structures means that you don't have to think twice about many of the things that should be purely mechanical. It then lets you recognize things when they show up in disguise, and to concentrate on the higher level work, where the real work begins.