The reason you swap gears when going up in tire diameter is due to how gears work.
It's not just for a "lack" of power or so it feels better. Lower gears, with larger wheels, also have the effect of being harder on the drivetrain. Think of it like riding a bike with gears. If you put it in a gear that's really hard to pedal, it'll be okay once you get up to speed, but at low speeds, like being off-road, you are putting tons of stress on the gears and chain and cranks and yourself by using that hard to pedal gear. Put it into an easier gear, and you trade off some high speed, but it's so much easier on you at lower speeds, and you're not having to crank down on the parts, either.
Sure, low range can help off-road, some, but it's a band-aid fix, using low range to get a slightly better ratio you should have in the first place. When you actually DO need a LOW range, you won't have it, since you're using low range just to have the ratio you actually need. You also wear stuff out quicker if you're always in 4WD and always using the transfer case for such things. Stuff doesn't last forever, if you use it ALL the time it will wear out and go out far sooner than if you just use 4WD and low range when necessary.
If you have stock 3.73 ratio gears already, I would say 31's are what you should stick with. If you have 3.27 gears, 31's are already pushing it.
It's your truck, you can do what you want and spend what you want on it, I would just say for the money, throwing 33 inch tires on it is not going to do much. Bear in mind that the clearance increase you get is only half of the increase in the tire diameter (only the bottom of the tire increases the clearance), so going from 31's to 33's, you just get MAYBE an extra inch of clearance, at the cost of what you pay for the tires, and the additional weight and effect on the drivetrain.
The aluminum covers don't dissipate heat better just by themselves, but there are certain "performance" designs used on Mustangs and other vehicles with the Ford 8.8 that have cooling fins that will act like a heatsink and give better cooling, sure. Carrying more gear oil helps a bit for heavy-duty use, but if the gear oil is hot, it doesn't matter very much if there's just more of it. Overall though, sure, with larger tires, and more severe use, you'll be helping out the drivetrain with more gear oil capacity and better cooling. For most people, just changing out the gear oil and using good brand name stuff is fine.
