The order of operation is a convention by human to communicate their idea, specifically about how to interpret expressio. Mathematicians don't just go around and pick an inefficient convention; expressions are arranged so that's it's easy to visualize how it works. The rule of thumb is, if it looks closer together and not separated by separators, you are supposed to combine them first. This is still true at even higher math when you have even more operators.
Look at a fraction. What looks visually related? The top looks like one group, and the bottom also looks like one group. The last term of the top is far from the first term of the bottom, so you don't visually group them together. Not to mention, a horizontal line looks like a separator, because people frequently use line to separate things into 2 sides.