When you break into someone's home you want to be ready for people with guns shooting at you.
Politely giving them a few seconds of free shooting before you draw your guns is not a great survival strategy.
> When you break into someone's home…
So we're starting right off the bat with the false premise that this is the only approach cops can take in these scenarios.
Best to kill anything that moves; it's the only way to survive.
If you break in with little to no notice or with a lack of manpower or if the occupant has nothing to lose, sure. This is why no knock raids are incredibly dangerous for all involved and generally a terrible practice.
With the number of officers they often have in most cases it would make more sense to start off slowly and unarmed, making an earnest attempt to communicate with the target. People won't usually choose to fight a suicidal battle. Even if they're extremely upset and disagreeable almost everyone will go along with it if calmly presented with a warrant and given some time to think things through.