Oh, I do see what you mean alright. And yes, that would be another possible convention.
As a matter of interest the convention you suggest (just start on the left and work through the sums) is actually used by some computer programming languages.
Hmm, you've got me thinking now. I wonder why that simpler convention not used for paper and pencil workings. Hmmm.
I suspect because it is actually easier in practice to see the effect of a change in the expression (say, add a new term or two) with BODAS.