I don’t believe any of the comments below address the meat of your question - what value are you getting from the equation ? I would answer- not much. You can

I don’t believe any of the comments below address the meat of your question - what value are you getting from the equation ? I would answer- not much. You can think of BS as a curried function. Since all the other params are fixed, you can curry and get a reduced equation that only depends on IV and underlying. If you do that, then its just - you give me iv and underlying, i give you spot. So, for a given strike(fixed), with the prevailing time left(fixed theta) under current interest rate(fixed), given the underlying, the historical vol gives you the wrong spot. You fudge it until you get the right spot. Call the fudged quantity the IV. Now plot that fudged quantity for a few other strikes and you get a smile. Then you can mess with that smile, plot the vol surface etc but end of the day, does the BS equation matter if the price of spot is going to be off and you have to fudge it with IV ? Its a good question. From an operational standpoint, the equation doesn’t matter. You can use bopm and get a more intuitive price anyways. Traders can trade the iv without knowing what effect BS has on the system. When I was in 5th grade, they took us to the top of a tall building. We dropped a ball and measured the time it took to hit the ground. So if you square that time and multiply by 5, that’s how tall that building is. At that age I thought wow this is such magic! Then I grew up and reached 8th grade and worked out equations of motion with some basic differential calc, and derived the canonical equation s equals ut plus half at square. So since u is zero and a on planet earth happens to be g which is 9.8, half of which is about 5, that’s why 5t^2. ok but does this equation matter ? I could have gone my whole life measuring height of buildings without knowing what is gravity.