We didn't figure it out; we agreed to a single order so that we can all communicate math effectively. This is the same way that we generally all use the English sentence form "subject, verb, object": I ate the bagel, you saw the fox, the car sped by us, etc.

Changing that order can introduce ambiguity: "Saw, you, the fox" is unclear who is doing the seeing. However, it can also be interesting in terms of drawing attention; look no farther than how Yoda in Star Wars talks. He uses a very different sentence structure, which is clear enough to not be ambiguous, but is also different. If everyone spoke like Yoda, we could still communicate effectively, even though the form of the sentences are different. So long as we all agree on how to speak, it works.

Likewise, if we did PASEMD, so long as everyone agreed to use the same order of operations, we could still do math. We'd have to change our current math formulas to match the new system, but the math is still correct.