HD,
Because it enables you to check the accuracy of the altimeter in the radio room, and also the radio op. Bear in mind he is a radio op, not an ATCO, and at one time did not need any experience or instruction in aviation matters in order to get the job. I remember one who had never heard of the term QFE, for instance, and was told of another who was busy looking in a drawer for said item.
QFE is universally used, QNE was supposed to be a safety bonus.
A question for you: Can you explain why La Paz cannot use QNH?