I could reword the first phrase of your question:
Considering that pitch goes down from high E to low E through all 6 strings (...)
When pitch is concerned, we never really consider "low" to come before "high", or the other way around. Leftaroundabout made a good comment about that: when guitars were still held in a more upright position, the strings were ordered from high to low, left to right (from the player's perspective). However, the piano (which is one of the most prominent instruments throughout history of music) has keys ordered from low to high, left to right. This indicates that there's never really been a link between "low to high" and "left to right"/"first to last". The order of notes/strings is just a matter of what is most convenient for the instrument in question.
A convention that we do have in notations and reading (or at least, Western culture does), is that we read everything from top to bottom. Scores as well as tablatures have the high notes on top and the low notes on the bottom, and I think the analogy can be found there. When we see a chord, our instinctive reaction will be to read it from top to bottom, which means that your highest string will come first, etc. (Note: this is just a habit we have because we have learned to read everything this way. A trained musician will of course read bottom-up in case they feel this is easier.) (Second note: this is just my speculation. Somebody with thorough historical knowledge will probably be able to provide a better answer.)