It's not only the bloodflow etc that's not symmetrical, but many of our organs as well. We have two off some organs, but only on of many and they are not all on one side.
To get some proper facts I googled it and this is what came up on "kidshealth.org"
"Some doctors specifically recommend that pregnant women sleep on the left side. Because your liver is on the right side of your abdomen, lying on your left side helps keep the uterus off that large organ. Sleeping on the left side also improves circulation to the heart and allows for the best blood flow to the fetus, uterus, and kidneys. Ask what your doctor recommends — in most cases, lying on either side should do the trick and help take some pressure off your back.
But don't drive yourself crazy worrying that you might roll over onto your back during the night. Shifting positions is a natural part of sleeping that you can't control. Most likely, during the third trimester of your pregnancy, your body won't shift into the back-sleeping position anyway because it will be too uncomfortable."