Interesting take Brian. For me this is a favorite Bay Rum soap/splash. Though I agree that it’s not pure Bay Rum. Try wearing just the splash and in an hour or so after application the Bay Rum character of this set really shines through (and lasts several hours for me).Tip of the hat and a nod to the “old school.” The soap and AS are an homage of sorts to the old Gillette in a can. Definitely get the shaving cream vibe ala Rive Gauche - but with a hint of bay - though it is definitely not a bay rum soap.
Also, just to be annoying and pedantic, I think the scent is supposed to be a nod to this Gillette in a can (shaving stick that came with the Gillette Old Type traveling/combination sets):
Not the Gillette Foamy