• “Wrong answers” only according to our current order of operations

    No, according to arithmetic.

    math still works if you, for example, make additions come first

    No, it doesn’t - order of operations proof. The only way it could work with addition first is if we swapped the definitions of addition and multiplication around… but then we still have the same order of operations, all we’ve done is swapped around what we call addition and multiplication!

    there is no ‘high truth’ behind it.

    There is when it comes to order of operations.