Newly Retired D-I Coach wrote:
Drills make you good at......
drills. Running makes you good at......
running.
Of course you shouldn't focus on drills to the extent they become a replacement for running. Running is the best exercise for getting better at running. In fact, short sprints (up and down hills and on level surfaces) can effect almost every change the explosive drills can effect; moreover, sprints are vastly more running-specific. You should include short sprints at times. But drills can be a helpful part of a dynamic warmup routine. They require different recruitment patterns and distribution of impact, so (if properly applied) they provide refreshing changes to normal forces to the legs while still allowing you to warm up and get in some exercise that can train you to reduce the time you spend in your plant phase.
In addition, the different combination of neurons activated and the variety of forces encountered can be helpful in injury prevention; for example, if you suffer a misstep while fatigued, you may be better able to withstand the unfamiliar stress or immediately and subconsciously correct for it mid-step. Summoning new recruitment patterns can also manifest itself in races which feature sudden pace changes. Faced with sudden physical stress when already fatigued, it's often difficult to make good decisions (or enact them if you do decide to make them), so the introduction of a variable set of neural patterns to your protocol can be of benefit (unless the time spent on it eats into your acquisition of basic running fitness, of course).
I'd say running drills are at least as important as stretching and calisthenics. You shouldn't expect to become a better runner by stretching alone, but you shouldn't completely avoid it. Likewise, pushups, pullups, ab work and other upper body exercises won't make you a good runner by themselves (otherwise, gymnasts could hop straight off the pommel horse and be good distance runners), but people who are muscularly weak normally have less vigor, stability/balance, posture and basic health than athletes with reasonable muscular fitness, so you don't want to be a grade A weakling. Flexibility and upper body muscular strength should be afterthoughts for runners, but they shouldn't be non-thoughts. Neither should drills.