I haven't noticed anyone explaining what different folks might use the deep drop position for. I don't use it for much time. I climb on the hoods, various grips, and a bit back. Trying to keep the weight off my thumbs, using a deep wrap. On the flat stretches I rest on the hoods or tops and pull either bent elbow on the hoods or in the drops. Often alternating. My dropped position is pretty low. Most important, I corner hard and descend in the drops. That's where the bike really handles, where I can tweek it around corners far better. Where it's really fun. So that's not as much time as climbing, but in the areas I ride I'm in the drops about 30% of the mileage. The fast part. I really like the drops for curves. I can see more easily. In the straight and fast stretches I settle for seeing badly. Have to have my shades on just right. But my muscles work right when I'm in the drops and I get less air resistance.
I suspect one needs to build up structural fitness and have a very well balanced position. I can lean against a wall on my bike, then bend over from in the saddle and touch the ends of the front QR. And straighten back up (the hard part). I figure as long as I can do that I'm fit enough!