Why is leg speed important? Leg speed, a.k.a. foot turnover is all about efficiency. To go faster with less work is the goal. Obviously a good strength base is needed, much of which is built prior to the meat of your racing season.
A very simple drill is 30 seconds on, 30 second recovery, pedaling as fast as you can in a low gear without bouncing in the saddle. I repeat: Without bouncing in the saddle. Bouncing means your pedal stroke is incorrect which will teach your body (more specifically your nervous system) bad habits that will lead to further problems. So spin as fast as you can while staying smooth and stable. Technique is every bit as important as the drill itself. High-cadence intervals of various durations can be used for continued improvement.