Here we report a series of objections to the mechanism of polymer crystallization by secondary nucleation plausible but for very mild cooling conditions, i.e. when solidification time is long enough or when the molecular weight, M, is not too large, conditions not preventing segregation at the growth front to take place. With a manichean approach, if otherwise time is controlling, e.g. in polymer processing, or M is large, segregation is precluded and accumulation of topological defects takes place in the amorphous phase preventing sequential growth of crystalline domains. A non crystalline phase forms very much departed from equilibrium, constrained by the crystalline domains and frozen to an extent dependent on the morphology developed. Consequences are discussed, themselves a proof that segregation simplifies topology when crystallization conditions are mild. They are collected from our own experimental evidence and from the broad, albeit often overlooked, literature on subjects intimately connected to crystallization and therefore spanning different fields of polymer science. Briefly we cite: • the extended crystallization range of a PET when blended with an oligomeric plasticizer, • situation arising as well for a broad MWD iPP internally plasticized by its own low M components. • The onset of a nodular morphology in iPP in an extended range of cooling rates even in presence of alfa monoclinc phase. • The time and initial structure dependent evolution of morphology of iPP when solidified at high cooling rates, probed by SAXS, WAXD and density, apparently leading to a simple t/T rheological behavior of the non crystalline component. In conclusion if demixing at the growth front controls crystallization under processing conditions then the high cooling rate solidification experiment is but a peculiar transient rheological measurement. Implications of this view are far reaching as the crucial role of the melt before solidification is evident