That's what I have always been told as well. I have found, for me a least, that I can almost balance the camera/lens on a monopod in most cases. So for me, that has been better than just handholding. My hands aren't as steady as they once were. I'm making the assumption here that you aren't a young pup, based on your years of experience, so I'm not trying to be contrary or to contradict you. You probably have far better camera holding technique than I do and your hands are likely far steadier than mine.
Kim (the male variety) Canon 1DX2 | 1D IV | 16-35 f/4 IS | 24-105 f/4 IS | 100L IS macro | 70-200mm f/2.8L IS II | 100-400Lii | 50 f/1.8 STM | Canon 1.4X III
RRS tripod and monopod | 580EXII | Cinch 1 & Loop 3 Special Edition | Editing Encouraged