I am curious why any beginning classical guitar curriculum would start on the 6th string. I assume that these beginning students are learning to read music as well. It seems to me that starting on that string would be harder than starting on the first string because of having to stretch the hand farther to get to it (though the thinnest string would cause more discomfort to the finger tips.) Also, it requires a lot of ledger-line reading when students are just starting out learning to read music. Wouldn't starting on a string that has notes on the staff be easier? What is the benefit of starting on the 6th string?
Where is this "classical guitar curriculum" that starts on string 6? Perhaps give an example that supports the statement. I just pulled Carcassi, Romero, and Parkening off the shelf and there are significant differences between how these players approach teaching.
First off, none of them do what you suggest in teaching the 6th string first. The closest is Parkening whose first lesson is a set of exercises on the OPEN 6, 5, 4 strings. This is not a great strain to sight reading as you are only reading the open string notes and playing open string bass lines.
Carcassi does NOT start on the 6th string by any stretch of the imagination! But he does start with the Key of C in its entirety. This does require reading everything in that key. The approach Carcassi takes (and this seems to have been a de facto standard for close to a century) is to introduce keys one at a time each with a basic scale, a cadence, a simple scale exercise, an arpeggio exercise, then 2-4 short etudes of varying style.
Romero's very first set of exercises is the famous Giuliani exercises. This involves playing a fixed right hand pattern over the C and G7 chord forms. The purpose is to introduce exercises designed to build skills in the two hands. This does not necessarily require sight reading skills.
That being said it has been my experience that in a first guitar class one is introduced to a set of exercises for the fretting hand that are meant to help develop independence of movement in the fingers. A similar set exists for the right hand, and using a pick for modern guitar. Regardless of the sight reading issue you perceive might exist the main task is getting the student familiar with correct posture and body movement.
All of the above mentioned approaches serve this purpose, to get the student's body familiar with correct execution of right and left hand finger movements, develop calluses on the fretting hand fingers, etc. The basic exercises might be written in SMN but that is not really the point of them in the first place.
When it comes to actual etudes, all of the above start reading melodies in the top strings.
There are some reasons why it is better to start with EVERYTHING at once (I won't take the red herring that string 6 is first, or string 1 for that matter). Each string feels different and it will take a different touch to get the same tone from each. The exercises in Romero's book specifically state that when one is doing chromatic trills up the neck on each string the goal is for each execution to have the same volume, etc. It would be counter productive to learn technique on string 1 and 6 months later try a bass string. You'd have to start over! None of your tactile response would carry over. This is why the basic beginning exercise are taught on ALL strings at once, not just 6 or 1.
I would say that trying to reach for that 6th string should, with the help of a good teacher, develop the posture needed to get there without "stretching" or overexerting yourself. These exercises are about technique and that is a big deal in the classical approach to the instrument. And, the sooner you start correct technique the less bad habits you will need to correct years down the line.
Another point is that from day one a classical guitarist needs to learn to coordinate bass lines with melody, to use the thumb and fingers of the right hand together. The Giuliani exercises help with this, and Parkening's book seems to focus on the thumb by starting with OPEN string 6, 5, and 4. The goal is not to leach ledger lines, the goal to get the thumb able to jump back an forth from one bass string to another without screwing up. Then come the fingers (i, m, a) on the top strings. From one point of view it is EASIER to start with the thumb. Carcassi does as well, but not the same way that Parkening does.
Easy is in the eye of the beholder.