Why are vestigial structures considered critical evidence of evolution?

Regressed (those which stopped growth only to be overtaken by other parts' growth) structures show a common descent.  Why would whales produce hind limbs, almost indistinguishable from those of other land vertebrates, as embryos, but have them overgrown before the bones form unless they were descended from land animals?  We see features from one group of organisms appear and regress in numerous organisms (eyes in cave fish, wings in kiwis, etc.).  It should be noted that vestigial doesn't mean absent.  Sometimes structures are reduced and find a new role.  Some snakes (the group including boas constrictors) have small remnants of hind legs that they use in mating.

vestigial structures are considered evidence because scientists believe they are structures that were once used by a species ancestors but are not longer needed. these structures do not impair the organism in any way, so there is no need for evolution to get rid of them. for example, the human appendix is considered a vestigial structure. it is believed that in earlier humans, the appendix helped to break down foods like plants. The appendix now has no function. Snake skeletons also have pelvises, suggesting that the ancestors of snakes had legs. The pelvis has no function in modern snakes, but it does not impair them in any way so snakes with pelvic bones are able to mate and reproduce and pass on their pelvic bone genes to the next generation.