I concur with the comment that the premise is wrong. I'm sorry if your teacher taught it incorrectly, but my teachers and those of my children taught addition and subtraction as being at the same priority and therefore to be evaluated left-to-right. Likewise for * and /. The rules are there so the students know what the right answer is, to enable experimentation with the other properties (e.g., distributive and associative properties).

Teachers in the United States do not teach to do addition before subtraction. They teach those as "equal" operations that are worked left to right. The same goes for multiplication and division. A scientific calculator will do the same. Your premise is wrong.