No one is saying a BC doesn't work. I started diving with one and I've used them over the years as rentals. But I greatly prefer a BP/W because I want to feel like I'm flying underwater. I'm still the kid I was in the deep end of the pool wishing I could stay under forever. When I dive I do barrel rolls and flips and stand on my head and lie on my back midwater to enjoy the sunlight. I fly low and zoom up over coral heads. I have fun, dammit. To do this I want my gear stable, but not constrictive. I want to feel free. I hate the BCs cummerbund and chest strap and single cam strap and all that extra fabric around my chest and torso. I don't want a bear hug when I need to add air to my wing. And I don't want a bunch of weight on my waist flopping around as I maneuver.
The main reason for this being the way the wing wraps around the cylinder(s). Buoyancy is above the centre of buoyancy, so the rig is stable. A backplate, harness and wing is frequently cheaper than a full-on jacket BCD with all the bells and whistles - removable weights, clips and dumps all over the place, etc.
You don't need padding; a one-piece harness will do; a stainless steel backplate (or ali if warm-water diving) is cheap and just buy the thing second hand. The wing's the most expensive component, but there's a lot of very good lower priced ones around. Avoid any wing that has the word "tec" emblazoned on it. That's generally a sign that it's not.