Roughly translated from Roberto Akira's website.

Roberto Akira is a Brazilian chemist who, after retiring, began sharing the knowledge he accumulated during more than 40 years working in chemistry.

"Cold process soaps are beautiful and easy to make, but every ingredient added to the soap is exposed to the saponification reaction and its highly alkaline environment.

A common belief is that oils added at trace are protected because most of the lye has already been consumed. In reality, much of the saponification is still taking place, so the oil added at trace becomes part of the overall superfat rather than remaining as that specific oil.

For this reason, adding a specialty oil at trace does not necessarily preserve the unique characteristics of that particular oil in the finished soap.

In hot process soap, specialty oils and butters can be added after the cook, when saponification is essentially complete. This allows a much larger portion of those ingredients to remain unsaponified than if they had been added before or at trace."

Hot process soaps may not have the intricate designs that make cold process soaps so beautiful, but for me the trade-off is worth it. I choose HP because it allows me to finish each recipe with a carefully selected blend of oils and butters after the cook.