I do see several advantages to a BP:
a) fabric BCDs, be they jacket or back-inflate, are generally positively buoyant. That translates to an additional weight requirement for the diver, unless they are inherently negatively buoyant, which most of us are not. In contrast, metal backplates with simple harnesses are usually negatively buoyant - unless that is altered by the additional of (unnecessary) padding- and the total weight obligation for the diver is less;
b) a metal backplate places much of the weight of the BCD where it optimally belongs, adjacent to the diver's center of lift (thorax / lungs). If you have a 'floaty' fabric BCD, even if it is weight-integrated, the weight is usually placed below that center of lift (e.g. on the waist on a belt, or in pockets at the bottom of the BCD). The use of trim pockets on cam bands - for jackets, 'soft' back-inflates. and BPs - has helped correct this to some extent, but it remains an issue with regard to trim. You can be perfectly weighted, but the distribution can still be 'off' and create a foot-low diver - a 'Forty-fiver', if you are adding a substantial amount of weight to compensate for the 'floaty' fabric;
c) wearing a SS BP i need virtually no added weight in certain configurations (fresh water, salt water with AL cylinder and 1 mm exposure suit), or i only need a minimal amount of added weight;
d) the plate is versatile, and allows for changing the lift (wing), to suit different exposure suit / weight combinations (e.g. diving both warm and cold water);
e) the BP is amenable to easy addition of a crotch strap, which serves to enhance the security of the scuba unit to the diver, and the overall stability of the rig. Yes, you can add a crotch strap to a jacket BCD with a little sewing (yourself or a shoe repair shop) and I have done this with two jacket BCDs over the years, so that is not an exclusive advantage of a BP. But, it is easier to add a crotch strap to a BP than a jacket;
f) I find it much easier to properly fit a BP with a single piece harness to a variety of torsos (mine included) than it is with a jacket. A perfectly fitting jacket is great. Getting a perfect fit with a jacket may be a bit more challenging than with a BP.