The TP based caster would be Dancer. The existing casters in the game at the moment are all entirely magic based with no physical training. As such any of the existing casters using TP for anything besides sprinting makes zero sense as they do not train in any skills that use physical exertion or dexterity.

OP you have some arbitrary obsession with making every job use every resource in the game. They don't have to and they shouldn't because it doesn't make any sense. Some jobs use both resources, some don't. Hell SMN, SCH, WAR and MCH already have a second resource in the form of their job mechanics, they don't need another to worry about.