No real reason why this, blended well to a reasonable pH level, would not be as effective as what we have today.
We don't need to wipe off every drop of our skin oil every day in order to eliminate bad smells or function regularly and healthfully around others.
It may reduce your potential customers a bit, especially at a particularly crunchy farmer's market, but the soap will be fine :)
It works great, it cleans well and I haven't had any issues with dry skin since we started using it.
The only real downside is that we get a bit of soap scum in the shower, but it's manageable.
The point is that it's a very plain soap and goes back to the 14th century.
(I had linked to the English wikipedia article but it's the French one that has more details, sorry for the confusion.)