First, there is a difference between STAGE bottles and DECO bottles. A stage bottle contains gas, either bottom mix if running a "flat" profile like an openwater wreck dive or constant-depth cave dive, or a depth-appropriate gas for cave, where you may need to travel for a distance in or out at a depth different than the maximum depth (then it technically becomes a deco gas as well).
In any case, I frequently interchange these terms as well, but thought it should be brought up.
In regard to dropping bottles - if it is a stage bottle, well, that would be dropped in a cave at the point you don't need it anymore on the way in (either change in depth, or at a point where gas calcs dictate its drop). Since you are coming out the same way when using a stage, it will be there waiting for you to grab on the way out. If using a stage in openwater, you typically breath it down, saving your backgas, and then end your dive when the bottle bottoms out (or when your total gas psi dictates you turn the dive).
Deco bottles can be carried or deposited, depending on the environment and situation. First, you should never, ever, ever hang bottles underneath the boat. I don't care if it is primary or "backup/reserve" gas, hanging extra crap under the boat causes problems. If it is your primary gas, that is just plain dangerous, no matter how you try and validate it.
If something happens inwater, you may need to expedite your ascent and might miss the anchor line. Or, the boat may break away (along with your deco gas). If an emergency arises topside (or if the boat breaks loose), it takes that much longer for the boat crew to clear the boat so they can move to pick up a diver, etc. If it is a big boat and they miss someone's gear line and deco bottle, you can guess what will happen to the boat's screws when it is put in gear.
Even if they catch everything, you prolong an emergency response and "trap" the boat.
Personally, my deco bottles generally stay on me unless I am doing some tight penetrations or have some project that requires working. A lot of times I keep them on me as I am just too lazy to take the time to unclip/clip the bastards. I have even done penetrations (really swim-thrus) with them as most times there is plenty of room to move around and if entangled, 99% of the time it will be on the valve or SPG which is right under your nose and easy to rectify.
The Rouse incident is not really appropriate to use as an all-around example. First, they were seriously impaired due to the use of air and heavy exertion. Personally, if I was doing a penetration like that (and I have on other U-boats and wrecks), I would deposit the bottles right at the point of entry, so you would pass over them on your exit and not be forced to swim back to the anchor line or guess where they are if disoriented. Also, I would clip the bottles together so I would only need to grab one clip to secure them to myself. This allows you to expedite your ascent should the fit hit the shan.
Anyway, just some thoughts...
Mike