The obvious answer to this question is no! You can never be too strong, but if you focus so much on strength that your forget other avenues of training it can be detrimental to your performance. Unless of course you are specifically training to lift as much weight as possible. Otherwise, you have to make your strength gains transfer to the specific goals you have set. Analyze the needs of the sport or specific goal you are training for and start to ask yourself what really needs to be trained in this situation? Strength and general conditioning are the foundation to which you start to build the framework for your training program. Functionally, how relevant are double leg strength movements to sprinting movements? Not very. Think about what sprinting requires of the body versus what squatting requires of the body. A single leg strength movement more closely resembles sprinting in that sense. Not to say that squatting doesn't have it's place in the training regiment of someone who wants to get faster. It is to say that there becomes a point where someone who wants to be faster should stop chasing squat numbers in favor of other exercises. There is another situation where being too strong can lead to injury. This occurs when your primary muscle group in whatever sport you participate in is too strong for your antagonist muscle group. An example of this is with sprinters whose quadriceps are too strong for the hamstrings. The hamstrings in this case are not strong enough to cope with the forces produced by the quadriceps eventually leading to injury. In training you have to focus on the antagonist muscles to ensure that such an imbalance doesn't occur. By doing so you will more than likely see an increase in performance as well. So make sure you are aware of the demands of your sport and dial in your training program accordingly.
