Every core lift (squats-505, clean-175 ,deadlift-don't do) is essential to becoming stronger and faster.
This couldn't be more wrong (ok, I lied it could be more wrong). The one lift that gets the muscles used in a sprint to "fire" the most is the deadlift. When you sprint you are pushing up off of the ground with your legs in order to accelerate forward and upward against the force of gravity. Studies have shown that the force applied by a sprinter horizontally is one tenth that of the force applied vertically. While squats are nice and do help you to increase the force you can apply to the ground, you never actually lower your hips to that position while sprinting in order to push upward off the ground. While a proper deadlift starts in this squat position the only motion you are focusing on is the upward push off of the ground (not the lowering of your body with a ton of weight on it like in the squat). The only reason any of your coaches have told you (or the only reason they should have told you) not to do deadlifts is because most high school and many college athletes do them incorrectly leading to injury. So if you can learn how to deadlift properly DO deadlifts.