Here is a primary example why edged weapons v. non-lethals are dangerous to police officers. This article was published in American Police Beat

Officer Down
Stabbed Cop Mounts Amazing Recovery
Written by Robert Mladinich
On the evening of January 15, just hours after a pilot "landed" U.S. Airways Flight 1549 in the Hudson River, NYPD Sgt. Timothy Smith of the 101 Precinct in Queens responded to a seemingly routine job regarding an emotionally disturbed person (EDP). The police had been summoned to the location by the EDP's wife, who grew concerned when he started babbling incoherently while chopping vegetables with a knife. Armed with a non-lethal Taser gun, Sgt. Smith, an 11-year department veteran, knocked on the bedroom door where the EDP had sequestered himself.
The EDP responded by pulling open the door and charging him with a knife. Although Sgt. Smith was able to fire the Taser once, the EDP plunged the knife deep into his left eye. The near-deadly incident was all but obscured in the local news by the plane "landing" that the press had dubbed "Miracle on the Hudson."

Because the knife pierced Sgt. Smith's brain, he initially lost his ability to speak and walk. He endured numerous surgeries, and his doctors were doubtful that he'd ever be able to function normally again. Not surprisingly to anyone who knows him, Sgt. Smith proved them all wrong. On May 15, one day shy of his 36th birthday and four months to the day after the savage attack, he walked out of Bellevue Hospital on his own.

As scores of police officers serenaded him with "Happy Birthday," he stepped out of a wheelchair and walked about 20 feet into a waiting car. The hospital's trauma director described his recovery as "just about miraculous."
Ed Mullins, the President of the New York City Sergeants Benevolent Association, was awed by Sgt. Smith's grit and determination, but said those traits were the norm among his members. He was aghast over the fact that the EDP was on the streets in the first place.

Since 2001 the police had been called to his home 10 times to subdue him, and during that time he has been in and out of psychiatric wards for, among other things, starting fires and threatening neighbors. A mental health review stated that he "has a history of becoming agitated and aggressive in public" when off of his anti-psychotic medication. The question of how much force should be used in handling such dangerous individuals is always the subject of great debate.

"Each circumstance is different, but this guy was a ticking time bomb," said Mullins. "After this occurred the usual talk about enhanced legislation took place, but the bottom line is all of the legislation in the world is not going to change the decision for a police officer to shoot or not to shoot."

Right now Sgt. Smith and his family are most concerned with making even more progress after their "Miracle at Bellevue." The sergeant has expressed a great desire to get back to work - sooner rather than later. In the short-term, however, his greatest desire was much simpler. After seating himself in the vehicle that would take him home for the first time in four months, he was asked what he was most looking forward to. "Sleeping in my own bed," he said.

The only problem with your account is that the suspect who was killed allegedly approached officers with a pole. A pole is not an "edged weapon".

A person who is shot in the heart by a high caliber firearm will not be able to continue a swing with a pole with any appreciable velocity. In fact, people who get shot tend to be pushed backwards by the impact. Not much chance of a suspect who has been shot, with a pole in hand, stumbling forward 21 feet and doing any appreciable damage to anyone.

I pay my tax dollars for officers to be trained well enough to handle someone swinging a pole without killing them. Mace, Tasers, kneecap shots...pick your option.

Edged weapons: traditional and emerging threats to law enforcement

TRAINING ISSUES

The 21-foot rule, a dogma of law enforcement training, has held that at a distance closer than 21 feet, a suspect with an edged weapon in hand could stab an officer before that officer could fire two shots. However, one researcher found that an individual can cross 30 feet in 2 seconds and suggested that the person could travel 70 yards before succumbing to injuries created by an officer's firearm. (14) According to the FBI, "There is sufficient oxygen within the brain to support full, voluntary action for 10 to 15 seconds after the heart has been destroyed." (15)

This suggests that 21 feet is an insufficient safety zone during an edged-weapon encounter. Unlike shooting a firearm, lashing out with an edged weapon is a primitive, instinctive action that a subject can accomplish in that 10- to 15-second window. At the beginning of the 20th century while conducting operations in the Philippines, members of the U.S. Marine Corps found that insurgents Insurgents, in U.S. history, the Republican Senators and Representatives who in 1909–10 rose against the Republican standpatters controlling Congress, to oppose the Payne-Aldrich tariff and the dictatorial power of House speaker Joseph G. Cannon. , although fatally wounded in the chest, still could move forward and issue a final blow from their edged weapons, seriously wounding or killing Marines. These experiences support the FBI data that even after being mortally wounded, a suspect with a knife still can inflict injury or death to an officer.