There’s a saying in police work: “I should have been a firefighter.”
Whereas firefighters get paid to workout, sleep and eat three square meals at the firehouse, cops just don’t get those fringe benefits. The combination of shift work, poor dietary habits, lack of exercise, and chronic stress can really take a toll on an officer’s body. Before you know it, years go by. The officer makes detective, but he looks like Dennis Franz from NYPD Blue.

Cops are human just like everyone else, so they have the same vanities. When it comes down to it, most would rather look good than perform athletically. And yes, depending on your assignment or whatever call you get, police work can be an athletic event.
If I’m training an officer to improve his or her physical performance at work, then I train the officer somewhat differently from regular Joe Citizen. For example, I always stress the importance of performing deadlifts. You'd be surprised how often cops have to pick up a person lying on the ground. Usually it's some protester who wants to lay limp and do the "passive resister" strategy, but it could also be a drunk, an arrestee or a really heavy person that the Emit’s need help putting on the gurney.
The pull-up is also relevant to police work. My other clients don't necessarily need to do pull-ups, but cops do. The pull-up really works and strengthens the back muscles, particularly the last. When cops chase crooks down an alleyway and have to climb a fence, they essentially have to do a pull-up. When SWAT guys rappel down the side of a building, they need lat strength and the pull-up develops lat strength in spades.
The pull-up is also great for developing grip strength. After all, you have to hang on and pull your bodyweight. Grip strength is very important in law enforcement. When a cop handles a firearm (whether it be a sidearm or shotgun), he needs a certain amount of both grip and lat strength. Grip strength also comes into play when an officer has to grapple with a suspect and subdue him.
Unfortunately, most police officers cannot do a pull-up. And of those that can do pull-ups, few can do a pull-up with all of their gear on. What's worse is the way recruits are trained in most academies does not prepare them for the physical demands of the street. Frankly, I really despise the way police recruits are physically trained in academies. It's completely ass-backwards. Most academies have no weight rooms, let alone strength programs.
They make these young recruits run and run and run and do thousands of pushups. High rep pushups develop NO strength relevant to our line of work. None. And with regards to running: when you're out in the street and chase a suspect, you'll more than likely have to sprint. It's about speed. You ain't going to be running for miles. That's what the patrol car is for. That's why you have a radio to tell your backup, "He's coming your way!"
All that endurance training, with the running and calisthenics, really just takes away from an officer's strength, speed, and power. In the cop world, strength, speed, and power are what counts. That's how you end confrontations and chases quickly. As they say in the world of athletics (and in the world of illegal narcotics), "Speed kills.”
Now, to a certain extent you need endurance. But for cops, we're talking about strength endurance. We're talking about maintaining your strength for an extended period of time, such as wrestling with a suspect. But these "long" wrestling matches typically don't last more than a few minutes. If the bout did last longer, then I'd say the officer needs to brush up on his ground fighting.
If you want to develop strength endurance in a cop, then he’ll need to incorporate that element into his skills training. It has to be very specific to the job, though. For example, what is typically done at academies is to have a recruit trainee sprint up a hill as fast as possible and then have the recruit subdue and handcuff a pretend suspect waiting at the top of the hill. You'll find that a cop's fine motor skills deteriorate after a "balls to the walls" chase, despite having practiced his defensive tactics (DT) skills on the mat a thousand times before.
If you have a trainee regularly practice his DT skills after an explosive bout of physical stress (i.e. sprinting up a hill), then the trainee learns to work through fatigue. That's a far better way of developing strength endurance specific to law enforcement. Not running for half a mile or more.