Sequence distributions of hetero-polymers, such as RNA and DNA, are essential for information storage, catalyzing chemical reactions, and regulating functions in living cells and at the molecular origin of life. Since most possible hetero-polymer sequences are dysfunctional, a key question is which physicochemical mechanism can direct polymerization and the selection of specific sequences. Interestingly, phase-separated condensates were shown to direct various chemical processes, including polymerization of homopolymers, raising the question of whether condensed phases can provide mechanisms for sequence selection. To answer this question, we use non-equilibrium thermodynamics and describe the reversible polymerization of different monomers to sequences at non-dilute conditions prone to phase separation. We find that when sequences nucleate and polymerize, their interactions give rise to phase separation, boosting the enrichment and depletion of specific sequences. Strikingly, various pathways for sequence selection exist when maintaining the system away from equilibrium. These results suggest condensed phases acting as hubs for Darwinian-like evolution toward functional sequences.