Appendix P is not a complete answer to the nonlinear issue. It sidesteps the problem of setting a value for SL (the "sustained" stress) in the more-accurate limit for the expansion stress range (SA). But it requires more work in that the user must check the expansion stress range AND the operating stress state (in addition to the longitudinal stress due to sustained loads).
It's a good answer to a limited question. Unfortunately, many casual readers would assume that between CAESAR II and Appendix P, we have what we need to accurately model and evaluate real world (i.e. nonlnear) response. You still have real world variation on model parameters, design conditions, pipe fitters, and on and on.
A very sharp pencil does not improve the artist's eyesight.