I do add vitamin E oil sometimes, but have begun to think it is a waste in soap.
Topically, I would definitely use vitamin E, though. My plastic surgeon recommended daily use topically after I suffered 3rd degree burns at age 10. I followed her advice religiously for many years and still use it if I get a new scar, although I don't play with fire anymore (I actually wasn't playing with fire at age 10, btw.)
As a colorant I have recently started using beta carotene, but only as a colorant. I learned about it here only last month and really like the color it gives.
It would be good to remember that soap is a "wash off" product and that any type of benefit you are seeking from vitamins would be best suited in "leave on " products such as creams and lotions that has a better chance of penetrating the skin layers . It is also good to note that few oils are high in vitamins and minerals as well as anti-oxidants , botanical additives can give an extra boost as well .
ETA: Avocado Carrier Oil contains Vitamins A, B1, B2, D, E, and Beta carotene. It is classified as a monounsaturated oil and is best suited for dry skin conditions in topical applications.
Argan Carrier Oil is rich in vitamin E, carotenes, antioxidants and essential fatty acids, is used for massage, facials and as an ingredient in anti-aging cream.
Black Cumin has a high amount of A, B, and C Vitamins and minerals including potassium, copper, zinc and selenium.
These are just a few oils from my list that shows you that vitamins are already there in the oils and you just got to know the beneficial properties of the oils , and coupling them with the right botanical can boost the desired effects that you seek. [just MHO]
I finally found a bottle of vitamin E and I used it in my lotions the other day. I used to add it to my shea whips when I made it more often. I would not waste vitamins in soap though. Things like tea tree oil is one thing where it would still be effective some but vitamin e would lose a great chunk (if not all) of its potency to the active lye.
It's actually the second part of the table that is more interesting - only one is not affected by alkaline solutions, 4 are question marks, the others are all affected by alkaline solutions. As all soap is alkaline, heat is the least of our worries - even if you added it post cook in hp, or cooled the soap in cp to stop it warming up, the alkaline would most certainly impact the majority of the vitamin additions. I imagine it also applies to natural vitamins in the oils themselves