It's situational. Outside, open parking lot, nobody else around - you can keep your distance. Crowded store, apartment, kids in close proximity, changes the calculus.
At the end of the day they need more training across the board. I have a friend that does training with many precincts. Many of them are 6 month classes (for the cadets to become cops). Many of those months are doing paperwork and other administrative stuff. They're not trained on what to do when somebody puts their hands on you. De-escalation training, etc. It falls to the training officer...who you HOPE knows what they are doing, etc. This is also why the advent of the SWAT teams came to be - front line dudes didn't know what to do, have the right gear, and again, training.
Whitman in a tower, sure. Anyone remember years back that lady that drive a semi that was hijacked in DFW? Big OJ-esq chase down the freeway. SWAT dudes everywhere. What happened? They finally spiked the tires, and this scrappy old bird wrestles the gun away from this crackhead, and jumps out of the cab. The end. What did SWAT do that any well trained officer couldn't?
Another dude I know is a cop in small-town, AL. They don't have much of a budget, so most of the policemen are also SWAT trained. They do some wild stuff, that nothing a "dedicated" SWAT team would be needed for. Few examples he told me:
Trailer part. Old disabled vet had his grandkids over. Dude had a live grenade (Vietnam maybe?). Little kid finds it, goes outside, pulls the pin, chucks it. Goes maybe a few feet. It smokes, by the grace of god doesn't go off. Primer corroded. They roll in, just dig a hole, fill it with det cord, have their little robot thingy push it in the hole. Boom.
Live video feed from outside a house. News is there for a "most dangerous" fugitive on the run. Most wanted kind of stuff. You hear a loud bang in the background. They set det cord on the front door, breached from the back. Grabbed the dude. The end. Not Jason Bourne shit at all.
Another trailer part. Another old vet. Another kid involved. Can't make this shit up. Alabama football (pre-Saban) is losing, and this old fucker in a wheelchair shoots the TV. Teenager comes in, he starts popping rounds off into the ceiling from his old service-issue 1911. They come in. First question. Does he keep any other mags with him? They count the shots. Then calmly walk in, flip the chair. Cuff him. Off they go.
None of this is sexy or wild. Spend the budget on situational training and stress inoculation. Not on fucking MRAPS and .50 BMGs that they never use. And get some of these fat fucks a gym membership. Jesus, some of these dudes would pass out trying to tie their own shoes.