The cold air has a higher density so it always settles down, by installing the AC on top, the cold air can interact faster with hotter air, so the cooling process is much faster.
If you install the AC on the floor, the cold air, doesn't naturally travel upward, and even if it does, thanks to the density difference and the air flow of the AC, it then, would be less desirable for human being think about cold feet and hot upper body!
Usually the heat is coming from the outside not the floor, windows for example, they pass the radiation, and simplify the conduction so the heat rate transfer is higher where the windows are installed. In a ten feet high room, an AC should be installed at 8 feet high, slightly above the windows, so the cold air can interacte faster with the hotter air.
There is also a technical issue here, duo to condensation you have to accommodate an extra duct to redirect the water to somewhere else, if you level the AC with floor then you need a pump to let the water flow, however by installing the AC at the recommended height, the gravity does the trick.