> I don't know how often hostage scenarios as extreme as you describe actually occur in the USA

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.