The outsides of the housings between the BBS02 and the BBSHD are not double the width on the HD. However, since the reduction and the end-caps on the housings are roughly the same width, the HD might only be 50% wider (68mm BB vs 100mm BB), but the stator and magnet-rotor are twice as wide on the HD. That also means the HD has twice the copper mass. Knowing that would indicate the HD "should" be able to run twice the amps as the BBS02.
The BBS02 was known to easily run on 20A without any heat-stress, and using 52V meant it could provide a very reliable 1000W. Users who programmed the controller for the max 25A could feel the warmth, but if kept in the proper gear to keep the motor RPMs up, the mechanical end of the drive performed fine, and it didn't overheat at a very pleasing 1300W.
Then...the HD made its appearance. The aluminum housing was thicker and had bigger fins, to absorb heat-spikes, and then shed them. The double-wide stator (and copper mass) would like be able to use double the amps with no wasteful saturation, in order to get the max miles from your battery. There are enough users that we know for certain that...if you give the HD at least 3 gears to use, it will barely get warm at its rated 30A. The stock controller works fine at 48V and 52V. I feel this provides an opportunity for some interesting options.
First, let's find out the heat limits of this drive, that "should" be able to use up to 50A. As long as you keep it in the proper gear, and provide at least 3 well-chosen gears, a temp sensor would likely verify that it's doing just fine with occasional peaks of 50A. That being said, if you use 52V, that would be a peak of 2600W. Other drives have shown that 2600W will cause very accelerated wear on the chain and sprockets. That's not a bad thing if it gets you the hill-climbing performance that you need (like San Francisco?). If so, I recommend sourcing a cassette instead of a freewheel, you will need it...
But, to get to my point. If the drive can use 50A without wasteful saturation, and can survive that heat...a customer might consider using 48V or 44V, instead of 52V. This is because one of the wonderful features of a mid drive is the ability of the customer to change the entire gearing range with a simple chainring swap. Going to a lower voltage, will make the motor spin slower, but the wheel RPMs can be regained by a chainring swap (or left as they are if you're happy with the top speed).
How can that be considered a beneficial option? With today's high-capacity and high-current cells available, a lower series-count in the pack allows you to use a surprisingly small battery pack. Of course, if you want very long range, this doesn't help you. However, if someone had a full-suspension bike frame and you wanted to use a small triangle pack, there weren't many options, until now.
Still, nothing wrong with 52V...