Just FYI, there is MUCH better soap out there than Williams these days. Dramatically better in fact.
As best as I can tell, it’s because each type of blade has its own grind angle and sharpness. And each type of razor has its own angle that the blade cuts at, its own depth, etc…
So ultimately it’s an exercise of matching the right blade with the right razors to your own personal liking. I mean, I have a cheap Chinese butterfly twist-to-open razor, and it works fantastically with Feather blades. My actual vintage Gillette SuperSpeed, not so much.
That said, I think that like anything else, the hobbyists get bogged down in the minutiae, and claim (for reasons unbeknownst to me) that only blades forged by blind Polish monks in a salt mine, and soap made from the fat of white buffalo calves is adequate for a good shave. In reality, most razors work just fine with most blades. It’s only at the extreme edges- really dull or really sharp (like Feathers) where it actually is obvious.
My father still uses a shaving mug and brush and lately he’s been using “Van Der Hagen” brand soap. When my mother had trouble finding it locally, I was able to order six bars from Amazon for twenty bucks, so not terribly expensive.
I was a fan of King Shave (oil) for a while, but then found Weleda have a shaving cream that’s excellent for keeping the skin moisturised and avoiding any redness.
I expect any brand which incorporates natural moisturisers will give similar results (especially when using a quality and new blade), but I’m now a committed fan of Weleda.