Complementary to what others said, the order of operations is also a natural consequence of rewriting expressions to avoid ambiguity.
For example, $3\times 4+1$. If this were all addition, there’d be no problem, because addition is commutative and associative. To rewrite this with only addition: $4+4+4+1$, so you’re essentially evaluating the multiplication first to make it unambiguous. Same is true for exponents and other hyperoperations like tetration. And without choosing a set order multiplication and addition would lose associativity and commutativity, eg sometimes $3\times 4+1\neq 4\times 3+1$ (which would surely lead to problems in defining other functions elsewhere). It’s completely a choice, but does make things clearer and simpler, and as others have pointed out tends to be more useful.