I was referring to the method. Turn car on without starting engine. After dash has completed its initial light blinking, pull turn signal to flash the brights 5 times, then press the brake pedal 3 times. Wait. After a few seconds the battery indicator light on the dash will blink and then go steady. Then start engine.
I had replaced the battery on the Fist about a month ago, and last week had to replace the battery on my F150. I did not do the reset procedure, and they both worked perfectly fine after swapping the battery without codes. I performed the procedure of flashing the brights and pressing the brake pedal on both car and truck after I read about it to see what it did. The battery light did blink as it was supposed to. But There is no discernible difference before or after in how they start and drive. And I had gotten no check engine lights in either one. I would guess that getting codes or apparently even the vehicle not starting after a battery swap is the exception, not the rule.
However what I have read from different Ford technician Q&A sites is that not resetting the BMS can reduce new battery life by a year or more by not charging the new battery properly, lead to drivability problems because of not delivering full voltage to all the computers and shutting off the computers every time the car is shut off, leading to having to relearn or not saving learning. Those last couple of things can lead to check engine lights or even failure to start if severe enough. It all seems to hing on how bad the old battery was and how long you drove it while it was delivering low voltage and not receiving charge properly.