Star, I believe that the primary reason why single leg squatting such a large portion of a 1 rep max (I’m assuming 620 is a 1 rep max) is difficult lies in the fact that a degree of balance is required to execute the exercise. It is difficult to complete a unilateral 1 rep max exercise without the risk of injury, as one is put in a position of limited stability when performing the exercise. Rj also said previously that practicing bilateral lifting increases one’s proficiency specifically with bilateral exercises to a greater extent than does practicing unilateral lifting. Therefore, it seems reasonable that an individual strong in various unilateral lifts would be incapable of expressing this strength fully in the corresponding bilateral versions. It would seem then that expecting a display of maximal strength in the weight room is impractical when unilateral lifting forms the base for weights work. However, rj also said that he did not advocate approaching maximal lifting capacity and preferred lower weights, so the inability to fully express strength via a 1 rep max would be irrelevant.
After having said all of the above, I would definitely have to concede that I do not have the degree of knowledge that you or rj have on the matter and this response is based solely on my interpretation of what I read in the thread. Feel free to point out any mistakes I have made in my response.