First, Shrink Wrap and Cellophane are two different beasts. Second, neither one will cause soap to go rancid. MP or CP or HP or a blend of CP with MP embeds. None of them will go rancid unless bad ingredients went in first.
My CP soaps after curing and cutting I put into ziploc bags so they stay in good shape in my workshop as they wait to sell.
As for wrapping - I use shrink wrap for a number of reasons. To keep MP from sweating you *have* to wrap or shrink wrap it. For my CP bars it keeps them from losing too much moisture and shrinking if they don't sell for several months after curing. My goat milk soaps will sometimes have some significant shrinkage if I don't wrap them soon after curing. I've also found it helps with keeping them from getting ashy too.
The final reason is because shrink wrap is cheaper than boxes and they can still see the soap. It makes the bars look shiny and pretty and clean to me.
Bonus, as a former graphic designer for years it gives me the freedom to play with the labels and or wrappers to make them more unique or different if I want to since finding blank boxes that fit my bars is a nightmare and custom printed ones can get way pricey. I can wrap the bars vertically, horizontally around the long or the short end making them each have a unique look for a certain line. Like goat milk I might do a long side horizontal wrapper where a masculine scent I might go with a narrow vertical wrapper and if the top isn't 'fancy' no swirls or things then a wrap around the center horizontal short way gives more 'face' area for the artwork on the label if I want to go a little crazy on the art for the bar. Also, if you want to use a soap stamp on the front and use a die cut wrapper to show off the stamp you can, if you have a crafting die cut machine. The options are greater for packaging with shrink wrap I've found.
I know some of the others answered all with good answers about soaps going rancid, but wanted to give you my reasons for why I use shrink wrap on my soaps. Technical, economic and aesthetic reasons.