From my experience, trans people (for simplicity I'll be considering MtF here) can largely be grouped into 2 categories. First you have the people with gender dysphoria. Whether you agree that transitioning is the proper course of care or not, these people tend to just try to live their lives as the opposite sex and try to deal with their mental illness (non-derrogatory, just like we can talk about people with depression or BPD as having mental illnesses without being derrogatory) without drawing too much attention to the fact that they're trans. If you had a magic wand that would alter history and genetics and have made them born a woman, they would happily accept. This group wants to be women.
Second you have the AGPs/transtrenders/etc. These people loudly profess their identity as trans, fly their annoying flags everywhere, talk about pronouns, and are all around completely insufferable. If you once again had access to your magic wand and told them you could make it so they were born as a woman, they'd probably decline. This group wants to be trans.