Well one could say they can't imagine anyone wanting to cut the cord prematurely, potentially causing pain to the infant and depriving them of all the extra nutrients and oxygen contained in the placenta. It really isn't that disgusting, and no, you don't wrap it in saran wrap. Many people make a special placenta bag out of cloth, and they sprinkle lavendar and other oils on the placenta so that it smells good. The cord is often wrapped in most paper towels. If it was that gross and that much of a hassel, people probably wouldn't do it.
Most people don't just eat the placenta meat. They often make it into capsules to be swalloed, grind small parts of it up to make a smoothie mixed with enough stuff that you barely taste the placenta, cook it in a special way so it actually tastes good, soak it in water and then use the water in a sort of tea or elixir to be used for curing problems.
You seem to have some preconceived notions about lotus birth and placenta-eating that are absolutely incorrect, and it seems like this may be the first time you've encountered the ideas. There are some fantastic ideas out there for what to do with the placenta, recipes for it, and some great information about the benefits of lotus birth. I hope you will read about it before forming your permanent opinion about these concepts.