>Why couldn’t you just write it 5 x 12 + 2 and solve it all left to right?

Well, what if you are writing down the eggs you see, as you see them?

What if you spot 2 eggs, so you write that down, and then spot 2 cartons of a dozen, so you write that down.

Oh, dang, now you've written 2+ 5x12, and under your convention, that isn't what I meant (I've written 7x12, but I mean 2 more than 5x12).

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Or, what if you have a formula like: "D = 2*x/y + 5*z^2"

You might be working in a lab, , and your assistant tells you "I've measured x & y, they are 7 and 3.5 respectively."

You're waiting for them to measure z, and figure that you'll simplfiy your equation, and you work out the left term happens to be 4 (2*6/3.5=4).

So you write "D = 4 + 5*z^2" to keep your equations easy to read and lined up.

Oh, dang again! That isn't what you meant, you need to change the order around!

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I think it is better to have a convention where the order you write addition in doesn't matter, so that you can add things as you discover them/calculate them, rather than needing to reorder your equation every time.

You *could* do it, but I think if society did, we'd have more errors than using our current convention.