Well you have to decide if you want to make a natural soap or a commercial cleansing bar. I read the ingredients of SCI. It uses coconut and chemicals. You can create a natural soap without it. I think most spapmakers don't use it for that reason. Decide how you would like to define yourself as a soap maker. What's your brand and what defines you and separates you from commercial cleansing bars. P.S. if the word soap is not on the label, it's not soap. It's detergent based. In the U.S. the law defines soap as a product that made with lye. You can only put the word soap on your label if lye is used to make it. Good luck on your journey.
I don't have any problem with the OP's idea of mixing a synthetic detergent with soap. Like I said earlier, I haven't done it, but I don't rule it out as something I might try someday. I do make syndet shampoo bars with SCI as a main ingredient and no soap whatsoever.
I haven't lost any sleep over the "un-natural" nature of my shampoo bars, nor do I worry about my products being mistaken for name-brand commercial ones.
We don't know anything about the OP's reasons for asking this question, and I think it's unfair to offer a critique of philosophy and ethics without a clear justification for doing so. It's also important to note that the OP is from New Zealand, so US law doesn't apply.
I'd like to see this discussion get back to directly answering the OP's specific question. If we want to debate the philosophy and ethics of combar and syndet cleansers versus soap, I recommend starting a new thread with that as the specific topic.
I'll offer this from my reading about commercial combination soap-syndet bars (combar) --
A combar can be mostly soap (meaning lye-based soap) and a little syndet (synthetic detergent) or vice versa -- mostly syndet, a little soap.
The advantages of having at least some soap in a combar is the soap makes the product easier to mix, extrude, and form into bars. Soap is relatively inexpensive compared to the cost of the better syndets such as SCI, so it reduces the cost of ingredients. Soap in a combar also makes the bar less likely to crack, soften, or become mushy, problems common to all-syndet bars.
The advantages of having some syndet in a combar may include increased mildness of the product, better performance in hard water compared to just soap, lower pH of the product, better rinsability of the suds off the skin, and better lather.
I do not want to give the impression that combars are necessarily always milder to the skin and more lathery than soap. Just that combars might be, depending on the formulation and the person.
To give an example, Dove is a combar, and I dislike using Dove. The lather feels odd and the skin feel after my shower is also odd. It is also a pain to keep the bar dry enough between uses so it does not "melt" away fast. Given a choice between my lye-based soap and Dove, I'll pick my soap. On the other hand, given a choice between Dove and a badly formulated soap, I'll choose Dove.
I'm not opposed to making and using a combination soap + syndet cleanser and I'm not opposed to a 100% syndet cleanser. Just that pure lye-based soap has its advantages and strengths too. I may experiment someday with a combar formulation, just to see what it's like and how it compares to my soap.
I make both cp soap and syndet bars and love both for different reasons. I am interested in combining the properties of both to get the best of both worlds. If I am happy with the results I will post
It's all a science and we are all probably driven to find things out, thats my reason for trying new things.
**I ALWAYS wear a full dust mask when working with any powders including SCI etc, any powder can seriously irritate the lungs**