Technically, he wasn't sleeping it off. Sleeping it off would imply he pulled over, and parked his car somewhere. According to the report, he passed out behind the wheel. Fortunately, he was in the drive-thru lane, and not on the highway, when he lost consciousness. However, the police were responding to a complaint, not simply hassling some poor soul sleeping it off in a safely parked car.
He was blocking the drive-thru lane, and someone called in a complaint. Once the police arrived, they were obligated to determine whether Brooks was alive and well, at the minimum. Not rousting him wasn't even an option. Plus, once determining he was drunk, they couldn't just leave him there. They could, conceivably, decide to take him home, if they determined he wasn't a danger to anyone, but just leaving a drunk in his car is irresponsible, and could lead to Brooks causing someone else to come to a tragic end, not merely himself; if left unattended, he could've regained consciousnesses long enough to resume driving, and to kill an innocent family.
Should Brooks have been shot? In this particular case, we could second guess the cops' split second decision, forever. Should one of the officers standing around have had a taser on the ready, once Brooks started violently resisting, and have used it the moment he broke contact with the officers with whom he was scuffling? Sure, if there'd been more officers there (I'm not aware that their were, but if there were, they were definitely negligent). However, the cops can't just leave drunks in their cars, even when they aren't passed out in drive-thru lanes. If the drunk driver wakes up and kills someone, the cops who left him there will be responsible... morally and legally. Imagine your teenage daughter is on her way home from the prom, when she's killed by a drunk driver that the police left to "sleep it off." The officer who made that call would be fired, and he and the department would be sued into bankruptcy.
Should the man who violently resisted arrest, and attempted to flee the scene with one of the officer's weapons have been shot, though? Well, it definitely wasn't the best PR decision....but, I doubt the cop was thinking like a politician, while the violent "gentle giant" drunk was attempting to disappear into the night, with one of the officer's weapons. Also, if Brooks had succeeded in disabling the pursuing officer with the taser, he could easily have disarmed the incapacitated officer, and have killed the officer, his partner, or someone else with the ceased firearm.
Still, should the officer have shot Brooks? If he hadn't, Brooks would have gotten away with the officer's taser, or given himself a stroke trying(he didn't really look like he'd ever run longer than the length of a football field...but, who knows), and could've used the officer's taser on someone else(to commandeer another escape vehicle, possibly), and the officer would, again, be responsible, for allowing Brooks to escape with one of his weapons.
Think about it, if resisting arrest and attempting to escape are rewarded with failure to pursue and escalate, the passivity of the permissive officers will only encourage more violent resistsnce and escape attempts from suspects, resulting in the eventual loss of Iife and personal tragedy, among the thus encouraged suspects, and the officers who deal with them.
If this event serves a good purpose, it would be that it might discourage future idiots from violent resistance and escape attempted that could get them or others hurt or killed.
Let me ask you this: if Brooks had been sentenced to 3 years in prison, for felony DUI, had no prior violent criminal record, but stole the remanding officer's taser, and fled the courthouse on foot, would it be permissible to stop his escape by shooting him? If not, if he later attempts to escape prison, do the guards have your permission to attempt to stop him by shooting? You see where this is going? If the police and prisons are rendered completely impotent, by stripping from them the option of the use of deadly force, they'll quickly become incapable of either arresting or holding criminals who present the gravest danger to public safety. If there's no penalty for violent resistance and escape from custody, everyone will attempt both, at every opportunity. Then, we might as well disband the police