The gamma radiation is what makes the waste useless for nuclear bomb fuel refinement, as it's results will apparently still be high enough in gamma to fry the electronics necessary to operate the device.
The high energy gamma is not difficult to shield when talking about a building, but very difficult to shield when moving. That is part of what makes Thorium reactors a poor source for proliferation and smuggling. There is no “sneaking” backpacks of materials spewing high energy gammas.
It is a shame spallation devices are necessarily large as the “on/off” aspect is appealing. The LFTR design used since the 50’s is also good though. They turned that thing off every Friday night and back on again every Monday morning. Unheard of with conventional reactors.