I am also in law enforcement. I believe that all the opinions here have most of the bits and pieces of the "whys" LEO's do not compete a lot. I have a couple from my department that compete. I know of a handful of others from various parts of the state that like to compete. I was in police work for 22 years before I tried any competition and it stuck and I loved it. Others have come once or twice and no more.
Speaking for my department, our officers get a part of a weekend off every 4 weeks and a full weekend off every 6-7 weeks due to how the schedule rotates. Most of the towns around us get every other weekend off. Most are not willing to give up one of their two days off to spend shooting and I do believe it is because they are just not gun people. I am fortunate enough to have a M-F day work assignments for the last 6 years which has allowed me to compete and I am a gun person. If I had the schedules mentioned, I would probably not be competing or would only on occasion be able to compete. I myself can only go to two matches a month or my loved one is not a happy camper and the stress of arguing about it is not worth it.
I believe it is invaluable the gun handling skills, shooting on the move skills and all around safety awareness I have been able to learn and achieve in the couple years I have been involved in USPSA. We are a pretty active department as far as firearm training is concerned and with myself being one of the range masters, we have taught and developed many of these skills for our officers. We even hold one or two USPSA type stages at each qualification and the officers love them. But even with all that positive training and exposure, out of 76 officers, only two of us really compete. I truly believe as many have expressed. You are either a gun person or not. If you are, you might try USPSA or another shooting dicilpine and out of those that try, it still seems that a small percentage will stay with it. I am glad I tried and now I just can't do without it.