Your argument is circular in nature. The right answer is dependent upon the order that you do the operations. So you can’t use the argument that the order of operation matters. Because if you do the math not using the correct order of operations, the answer comes out incorrectly.
For example, we could just do away with order of operations all together and explicitly use parentheses everywhere. While the system would be extremely painful to use, it would result in a consistent mathematics.
So there’s nothing inherently correct about our current order of operations. I will say that I like it and that it makes sense to me.
If you want a fun Wikipedia trip look up reverse polish notation (RPN). If I have to do away with the current order of operations, I might look to this as a possible alternative.