The huge advantage of using the drops a lot. Less lost training time from spills happening because you hit something and you either lost control or your hands slip off the hoods. Quite simply, the drops are the most secure way to hold the handlebars. Even with completely relaxed hands, it takes a lot to dislodge them. True, a little less aero than arms bent, forearms parallel to the ground on the hoods, but that position should only be used when you can see up the road and you aren't to tired too react to what you should have seen.
I set bikes up to be ultimately comfortable in the drops, then position the hoods to optimize them. I also position the drops far enough forward or down that I can ride with my back close to horizontal with my arms almost straight. This means I have a comfortable bike that I can ride upwind for an hour or two tired (and will still be safe after I become considerably more tired

). Yes, the hoods would be faster for that long upwind haul, as would close drops and bent elbows, but when the bent arms gets too old/tiring, aero goes completely out the window whereas the long reach to the drops can be done in relaxed state for hous keeping my back low. For endless upwind stretches, that counts for a lot!
Ben