Sex chromosomes of mammals and most birds are heteromorphic, while those of many paleognaths (ratites and tinamous) are inexplicably homomorphic. To dissect the mechanisms underlying the different tempo of sex chromosome evolution, we produced high-quality genomes of 12 paleognathous species, and reconstructed their phylogeny based on alignments of the non-coding sequences extending to nearly 40% of the genome. Our phylogenomic tree grouped the South American rheas and tinamous together, and supported the independent evolution of gigantism and loss of flight among ratites. The small-bodied tinamous have much higher rates of genome-wide substitutions and transposon turnovers. Yet majorities of both have retained exceptionally long recombining regions occupying over half of the entire sex chromosome, with the rest sex-linked regions diverging from each other at a much lower rate relative to neognathous birds. Each species exhibits a punctuated sequence divergence pattern between sex chromosomes termed 'evolutionary strata', because of stepwise suppression of recombination. We concluded that all paleognaths share one evolutionary stratum with all other birds, and convergently formed between one to three strata after their rapid speciation. Contrary to the classic notion, we provided clear evidence that the youngest stratum of some tinamous formed without chromosomal inversion. Intriguingly, some of the encompassing W-linked genes have upregulated their expression levels in ovary, probably due to the female-specific selection.We proposed here that the unique male-only parental care system of paleognaths has reduced the intensity of sexual selection, and contributed to these species' low rates of sex chromosome evolution. We also provided novel insights into the evolution of W-linked genes at their early stages.