should thermal insulation ever be applied directly to the underside of a roof top?
yes its done all the time on metal buildings. works well but expensive.
On pole barns with metal roofing it is common to have a thin layer of insulation directly under the roofing. This prevents condensation from forming.
Should it be done, No. Thermal Insulation is put direftly above the ceiling. Not on the actually roof top. The reason being, that even though both methods will trap in heat, With the insulation on the arches of the roof, it still allowing heat into the Attic, Or roof space. This means that the top of the roof will infact be the warmest part of the house, and lot of heat will be lost. from the main rooms of the house.