Often. Mostly domestic violence barricading scenarios, which are usually handled by front-line officers with sidearms and negotiation. SWAT deployment is usually discretionary at such a scene, predicated on an active shooter, and anticipates forced entry. In an active shooter scenario, front-line officers will typically defer to SWAT to force entry, given the risk.
But yes, it does happen. A lot of domestic violence ends badly.
I'm no fan of wife-beaters, but somehow every other nation on earth has figured out less violent ways of dealing with them. Yes, in many cases "the way" is to simply accept that wives will get beaten. Admitting this is no more an acceptance of police violence than admitting that not all nations are governed with perfect justice would be an acceptance of all of our damned wars. This is a "won't somebody please think of the children?!" level of argument.
People can obviously do plenty of damage beating each-other with objects, slashing with kitchen knives, or whatever, but guns seem to lead especially often to escalation from shoving to instant death.
When police show up, if someone has a gun everything is a lot more difficult/dangerous.
I don't know how often hostage scenarios as extreme as you describe actually occur in the USA, but I read about instances of 'swatting' constantly. Given the false-positive rate of such reports, it's no surprise that sending military-style squads to 'shoot on sight' ends in tragedy again and again.