On cut pile....
I always put a groomer over wool carpets, because the wand tracks can set really badly when dry.
Nylon, I mostly always groom because the patterns are very distinct due to the pile being very flexible
Polyprop, almost never, the wand tracks don't show up anywhere near so much and the pile springs back almost by itself. Certainly after a little bit of foot traffic and a quick vacuum it'll be ship shape.
I Don't groom any loop pile except wool if the loops are quite big and wand tracks noticeable
By the way let's not forget the primary purpose of grooming after extraction - to stand/open the pile up which allows the water to evaporate quicker, shortening drying times