The best method was already stated, "man's gotta breathe".

The film over his eyeball is also protected. His eye sockets are vulnerable.

He'd go blind for a few minutes while dislodging the bullet(s) from his bones. Then his eyes would grow back and everyone would start vomiting and pissing themselves.

Probably because Diamond Back is a sick sick man and knew Luke Cage would die a slow painful death instead of finishing him off quickly.
No way Diamondback could have predicted the elaborate plan Luke would endour to remove the shrapnel, let alone meeting the only doctor who could perform the percedure.
Diamond back was all about making Luke Cage suffer as much as possible.

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They didn't have to know about the previous incident.
Literally nobody tried to shoot Cage at close range with anything greater than a small caliber pistol because reasons.
When he was raiding the gang hideout in Episode 3, Cage was wearing headphones. Anyone could have come up behind him and blasted him in the head with a shotgun.

They don't know about the previous incident. Even if they did, Diamondback did come along with the Judas which pretty much meant people could now shoot at Luke Cage from a distance with a bullet that was guaranteed to cause injury, and not have to subject him to a point-blank shotgun round. In fact, he'd have to probably eat the barrel of the shotgun or pistol for results.

As seen in Jessica Jones, his eye sockets are vulnerable.
A better question is why doesn't someone shoot him in the head with a shotgun?