I sent the link to this thread to one of the American gunsmith's you so easily dismiss.
I'm paraphrasing but here are his thoughts.
"Americans made checkering an art form. Not the British, nor Italians, nor Austrians, nobody but the lowly Americans.
Now the world aspires.
About the only reason that W&S did flat top checkering was that it cost them less to meet their price point."
FWIW: He is known well for his stock design and I trust his opinion without question. He has forgotten more about the making of classic rifles and shotguns than most will ever know.