When I first watched that movie, I closed my eyes at that scene. Its too horrible, and made me sick.
Recent reruns, I still do the same thing as the first round. Its disgusting what they did to the rat. And I'm not a fan of rats.
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Liquid breathers have the issue that all the equipment needed to remove the CO2 from the perflorocarbon and add the oxygen, as well as storing the extra oxygen for your dive, is bulkier than SCUBA equipment. Not something that is desirable when you are tying to be a Mer.
Rebreathers might well get small enough to hide all the equipment between your legs, inside the tail. Especially if you are willing to limit your dive to a short time, like 30 minutes. There would still be the issue of the air hose between the equipment and your mouth. It would not look very Mer-like.
Rebreathers need a lung to breathe into that is at least the same volume as your lungs. So no, they won't get smaller than scuba gear.