Mike makes a good point about the quality of Brazilian jiujitsu instructors -- being able to say "gward" and call everyone "my fren, my fren" does not a great instructor make. Most schools tend to teach to sport aspects, like the one at which I now train (it's the only one near me). My prior training in BJJ and Dog Bros involved a greater awareness of striking opportunities that aren't emphasized in sport BJJ. Striking makes a big difference in creating or leaving openings for techniques. That said, I feel that the Brazilian style has a solid matrix of ground fighting positions from which to work. The positions of guard, mount, side control, cross body, sit out, are a road map to where you want to take the fight. Every other position is just something on the way to the other positions. This type of organization provides a solid foundation for the fighter to organize their game plan.
For LEO's and other weapons bearing types, the BJJ emphasis on closing and going to the ground creates problems for weapon retention. It's hard to protect that weapon side at all times when you're rolling around on the ground. Likewise, rolling around can be difficult with a duty belt or bulky body armor. Helpful here is to remember to keep hard accessories like cuffs (the major offender on most belts) off the centerline/spine area. Though this should be readily apparent upon sitting down in the cruiser, many people seem to miss this vital subtlety for serious injury prevention. For LEO's, grappling is a part of everyday interactions with subjects. It's far easier to be well trained and be able to resort to grappling rather than only striking -- there's less 'splainin' to do after effecting the arrest.