The real reason why we do this is so that we can write DISTRIBUTION neatly.

(4+5)*6 = 4*6 + 5*6

See how I didn't have to write the right side of that with any parentheses at all?

If we had pure left-to-right order of operations, I'd have had to write

(4+5)*6 = (4*6) + (5*6)

which is much uglier.

Note also that * distributes over +, but + doesn't distribute over *:

4+(5*6) != (4+5) * (4+6)

So there's no advantage of less parentheses in assuming that + should be the first operation you perform.

Similarly, exponentiation distributes over multiplication. That's why the usual order of operations is PEMA:

P (exceptions before general rules)

E (^ distributes over *)

M (* distributes over +)

A