Well, everybody uses standard B-S to quote option prices, just like everyone uses interest rates to quote bond prices. But nobody prices options while assuming

Well, everybody uses standard B-S to quote option prices, just like everyone uses interest rates to quote bond prices. But nobody prices options while assuming all the good old innocent assumptions underlying the original derivation of the formula. That, indeed, can be seen from the fact that different vols will be quoted for different strikes at the same expiry.