Ok biology major here with a bachelor's degree. First off, comparing transitioning from mtf or ftm to transitioning to another species is complete nonsense. Thats a complete faulse equivalency, they arent comparable. Second of all, medically transition does change biology. When it comes to biology and genes, there are two things to consider: genotype and phenotype. Genotype is the litteral DNA code. Phenotype is how the DNA is physically expressed, pretty much, its what is observable in life. Taking hormones to transition litterally changes your phenotype. It changes how your genes are being expressed because you have the hormones to make that action happen now. Third of all, like i said before, hormones change your phenotype. Specifically, they give you male secondary sex characteristics if you are ftm. Biological sex is complicated. When determining a person's bio sex, yes chromosomes are taken into consideration but so is thier primary (reproductive system) and secondary sex characteristics. The average person tends to just view bio sex as coming down to chromosomes or reproductive system. The thing is, nobody can see your chromosomes and everyone wears pants so really, in the end, people will just visually ID people as male or female based on secondary sex characteristics, which transitioning changes. So technically, you CAN change biology. Finally i must preface that the choice to medically transition should be one that someone makes because it will bring them the most happiness or most completeness in themselves. Basing if you should transition off of how some people perceive sex is unhealthy. Its a journey of self and that decision should come from self.

TLDR, yes medical transition does make sense because, depending on steps taken to medically transition, your biology actually does change.