Actually it’s pretty much one the established methods to figure out body fat percentage - underwater weighing. You don’t actually need to measure the volume though to figure out the denisty.
What benefit could that possibly have over using just one regular scale for mass and a small tank with a volume scale to measure volume? 
Looks like what you’d come up with just to make your equipment look interesting.
Guessing but my thought would be that displaced volume (average human body 66ish liters but obviously a wide range) is more difficult to measure with great precision, and that measuring two items (weight and displaced volume) is going to unavoidably add in noise compared to a weight measure alone.
In any case hydrostatic weighing is now displaced as the gold standard by MRI methods which has the huge extra plus of being able to identify exactly which compartment the fat is in, even determining if internal fat is visceral or non-visceral and different levels off subcutaneous fat.
But of course none of these are very practical in an office setting.
More noise than calculating volume from underwater weight, a weight that doesn’t seem all that easy to get accurate since you have to do it three times and average it?
Measuring displacement is as easy as measuring how high the water rises when you add a body. I expect you could get that accurate with less fidling than underwater weighing requires, but I suppose that’s a moot point now.
What I’ve seen on TV is that people are put in a sealed capsule to measure body fat. I assume this works by adding a known volume of air and then measuring the increase in air pressure, as the air in the capsule compresses but solid and liquid mass doesn’t. So from this, you can get the amount of air in the capsule and thus the amount of non-air = body volume. All without getting wet! And without having to account for the varying amounts of air in the lungs that will throw off water displacement measurements.
Again, don’t know for sure, but my understanding is that the three times is for the variability of the lung expiration (which of course changes volume and density, less expiration and more bouyant force). Which you’d want to do in any case. Weight is a pretty precise and reproducible number.
Anyway as you say, moot. The point is that the concept was indeed valid and was used as the gold standard for total fat % until a better gold standard came along.
Wouldn’t it be more sensible to take the lowest number, rather than the average? If the idea is to get “weight if there was no air in the subject’s lungs”, the fact that there can’t be negative air in the lungs means the lowest number is closest to the desired result than the average.
Yes that would seem to make sense to me. Again, I cannot great knowledge about the technique.