Hmmm. I can only answer subjectively.
I am one to stretch the life of a blade I'm using. I recently completed the One-blade-in-Feburary challenge with a NOS Wilkinson Sword Classic blade. Thirty-one shaves. If one considers sharpness as a contributing factor to longevity, then I don't think sharpness of the blade is affected by the quality of the soap. But I do know that the slicker the lather, the better the shave, and therefore the longer I'm apt to use a blade. Certain soaps make me question if a blade is "done" or not. But that notion is usually dispelled if I seek out a soap that will provide the slickness I desire.
I tend to believe that when I use Williams, it makes my blades last longer. I attribute that to the extreme slickness of the soap. But I have no real data to back that up.
Vintage or modern Williams (or both?)
Wise words.A good soap that works for you will give you a more comfortable shave. This in turn might help you tolerate a blade one or two more shaves than with a soap that doesn't work for you.
It's your hair that dulls the blade. The soap (and your skin) contribute very little, in comparison. If you want your blades to last longer, make sure your hair is well hydrated so that the blade can slice through, rather than tug at the hair. In any case, blades are dirt cheap, so it's hardly worth worrying about longevity.