Parentheses do fix ambiguity problems beautifully. But they can also be a total pain if you have to write out a whole mess of them again and again and again.

The reason we have the multiply-then-add rule (rather than the other way around) is because "Add up a list of values-multiplied-by-quantity" is a super common kind of scenario - and this convention lets us shortcut away lots of parentheses from these often-encountered problems.

For example, imagine adding up the value of one penny, two nickels, four dimes, and three quarters... Writing out "(1×1) + (2×5) + (4×10) + (3×25)" is amazingly unambiguous and perfectly legible... but simply writing out "1×1 + 2×5 + 4×10 + 3×25" (and maybe leaving some whitespace for extra clarity) saves the work of two parentheses per list-item. Maybe that isn't a big deal when writing out a single list of only four coin denominations... but if you have to do hundreds of similar such problems then those extra strokes will definitely add up.