After installing a brand new radiator, what would cause the thermostat housing to blow off and be destroyed?

There is excessive pressure in the system. If bleeding of system was not properly carried, it would overheat and result in excesive pressure in system. The thermostat housing could have been brittle due to previous overheating issues and the pressure and overheating caused it to disintegrate. Replace with new, bleed system and have leak down test performed to ensure the head gasket is not bad.

After installation of all components, fill up with coolant. Start and run engine for 5 minutes with radiator cap off. Top up if necessary. Stop engine. Top up coolant. Close radiator cap. Run engine till radiator fan comes on. Wait for engine to cool down. Remove radiator cap and recheck coolant level. Top up if necessary. If level is very low, you would need to repeat above process till level is constant.

Leak down test is performed by applying pressure to the system and checking if the pressure drops. A special tool is used for this process and some parts stores loans them out.