Not only does it make so fucking sense for a character written in the 1850's to be trans, it makes no sense for Sherlock to be trans, and these examples given show a complete misunderstanding of the character's features and purpose.
Obviously it makes no sense for Sherlock to be trans. Binding, hormonal treatment, or even understanding of the existence of Trans people was nonexistent at the time, so there was no way for him to transition to male. He has also been described as being about 6ft tall, very rare for any woman, let alone a woman from 150 years ago.
Sherlock's dismissal of female emotions and frivolities was a hubris that lead to his intellectual defeat with Irene Adler in A Scandal in Bohemia (maybe he did it more times, I haven't read the series much, but I don't think this author did, either). His lack of socializing with men or women as well as his general dismissal with all things regarding emotion was because he was meant to be an unbiased, calculating, logical and observational machine.
"All emotions, and and that one [love]particularly, where abhorrent to his cold, precise but admirably balanced mind. he was I take it, the most perfect reasoning and observing machine that the world has seen, but as a lover he would have placed himself in a false position." (A Scandal in Bohemia)
Watson as a character added an ounce of humanity to the pair and made the stories more enjoyable for readers, but Sherlock's amazing inductive mind unclouded by human judgement and error figure out a complicated problem was the star and point of the series
REEEEEEE.