Seems like a bad habit to develop, IMO
EDIT: there are times you want to nose down into a landing and thats typically in short field landings, but you are probably never doing that in gulfstream
Pure conjecture here since I've never flown one, but decreasing thrust might actually cause a nose up movement. That and my experience with pusher prop planes which very much have this issue.
Thinking about the 737-max which had the opposite problem of engines low and forward, where increasing thrust caused excess pitchup.