The thing is, the hostage is the only bargaining chip that the criminal has.
They won't automatically shoot the hostage at the slightest police apparition, that would be them losing they only hope for a way out.
They would rather *threat* to shoot, and try to see what they can leverage to try to save their asses.
But once the hostage is dead, they'd lose all mean for negociations.
So the most likely way the situation unfolds would be :
*bang* *bang* *bang* "This is the police. Open the door, we have a warrant"
*keeps door closed*
"Stay out of here! I have a hostage! If you entire I'll kill them! And find me a helicopter and enough fuel to Cuba, or I start to chop fingers!"
*police calls in reinforcement, negociators, etc. and tries to find a way out that minimizes losses*
As opposed to the SWAT approaches:
*over armed and under trained police* [Storms in]
[all starting shooting everywhere]
[high risk that the hostages get harmed during the mess]