To be perfectly honest, I don't understand the need for a burqini. I'm of the firm opinion that it betrays an unhealthy obsession with sex to the point where someone else has to take measures so you don't feel the need to screw like crazed rabbits. Honestly, there is nothing remarkable about arms, legs, shoulders and the like---we all have them. Acting if that were different is silly cultural nonsense to say the least.
There's one application where a burqini might be genuinely useful: if you happen to have a skin disease, or lots of disfiguring scars from burns and the like, then such a full-body swimming outfit could very well offer you a chance to enjoy a day at the beach again. (Pools I'd avoid if the disease were contageous.) A burqini might be a bit more fashionable than a neoprene wetsuit---besides, the wetsuit has the disadvantage of showing all sorts of body curves: this sets the pervert's heart racing again, and we can't have that, can we?
However, the burqini is quite impractical from a swimming point of view: it's not very streamlined, it introduces tons of friction from air pockets and losely flipping textile, and once you emerge from the water you face the problem of having a few kilos of wet garment clinging to your body. Enjoy the next hour while you wait until it is sufficiently dry---given the rather limited effect of towelling wet garments I would recommend against wearing it unless it is well over 25 degrees C outside.
One little plus: it offers protection against solar UV radiation which does not wash away.