Thrust is related to how much air is displaced.
And you have never heard of downwash? Sorry facetious.
And you are saying that the amount of air displaced (downwash) is irrelevant if the aircraft is not moving relative to the earth. So in the helicopter example, although the blades are moving a whole lot of air and holding the helicopter up against gravity, that the Trust HorsePower is still zero, because we haven't gone anywhere? A force is being applied, but no distance travelled, therefore no work completed?
If that is the case, again I say that the helicopter example is a bad one. Because measuring THP for a helicopter is useless. Again helicopter POH's have very clear performance graphs that display hover in/out of ground effect charts to prove this. (Yes I know that these are a chart to provide a guide as to the helicopter performance based on expected SHP vs weight given certain Dalt)
I think in a scientific calculation you would say that although an engine is producing SHP there is no THP because we haven't gone anywhere, but in reality (a practical sense) you would simply describe that there is insufficient SHP being applied to create enough Trust to provide movement.