Sequencing is Ordering in Ranking determined by Value, Predecessor or Successor, Catalyst or Response, and Associative and/or Commutative Properties. 

I will be blunt, the only common denominator I can find as to *why* we have an Order of Operations is due to the Logical Order of Disintegration/Integration.

To date, I have not yet found any other reason anywhere in my research aside from my own Observations in which one reverse Engineers them in the correct Sequence of Comprehension from Disintegration/Integration.