I mostly CPOP because I have one halfway decent mold and I like to be able to free it up in a day or two. If I can ever get my hands on another one (or two or three), I just might be able to be more patient about it and let the soap take its own sweet time. I also like not being forced to wear gloves when I unmold it because I know it's fully saponified. Not that I'd want to use it right away, but I'm not worried about a chemical burn. One thing I will NEVER CPOP again is goat's milk or any soap with any kind of sugar content. See my post "I Shot My Eye Out!" and you'll see why.
I notice that mica swirls look very different with CPOP vs. straight CP. The sparkles seem show up a lot more. Some FO's don't seem bothered by CPOP and other disappear temporarily only to come roaring back later. It's one of the experimental aspects of soaping that I really enjoy. As for the EOs, I never considered the aromatherapy aspect because I assumed the lye would destroy it. I'd never promote a soap of mine as "therapeutic" anyway because I couldn't possibly prove such a claim.
As for HPOP, I can't imagine why you would hot process (cook the soap in a crock pot or on the stove top) and then put the mold into the oven, because when you cook soap, it's already gelled before it goes into the mold. Maybe someone else can explain that one because I'm baffled.