One of the things I've always hated about Hollywood's approach to superhero movies has been one of their techniques for condensing things into a two hour story. In order to explain a superhero and their arch-enemy in such a short period of time, they simply make them both come from the same place.
Superman has to fight Kryptonians. Batman's parents were now killed by the Joker. Spiderman suddenly got bit by a spider that worked for the Green Goblin. The Fantastic Four and Doctor Doom go up in the same rocket that got hit by cosmic rays. On and on it goes, when there are plenty of adversaries for any given superhero whose origins aren't linked to the hero at all. In fact, the best villains are those who come from a completely different place than the hero, just so they can be so much more . . . evil.
Sherlock Holmes has gotten the same treatment from Hollywood and its writers. Inevitably, Professor Moriarty has to be Sherlock's math tutor or professor, as in Young Sherlock Holmes. The Seven Percent Solution even took it a step further, making Moriarty's affair with Holmes's mother the catalyst for him even becoming a detective. Elementary undoubtedly gave it the craziest spin by making Moriarty the lover who "died" and caused its "Sherlock" to dive into his drug problem . . . although there is a strange parallel to 2002's A Case of Evil, wherein Moriarty faked his death and then addicted Holmes to heroin.
What is it that makes screenwriters want to link Sherlock Holmes and Professor Moriarty somehow? If that's something audiences enjoy so much, why not just have Sherlock Holmes born to a family of criminals and have him spend his career hunting down cousin Grimesby, cousin Sebastian, cousin Charles Augustus, and the like? Do we actually enjoy the hero-villain connection that much, so is it just a matter of screen time economy?
Personally, I'm a big fan of letting the villain have his or her own story and their own character development. Some stories have hero-villain connections at their core, like that of Thor and Loki. But adding them after the fact never seems to work out well, other than perhaps for novelty the very first time it's done.
Now that Sherlock Holmes and Professor Moriarty have both been freed up in court (interesting how Moriarty always winds up free after a day in court, even in our world), I hope future creators will let them keep their separate backstories. There is so much more material, and fun, to be had there.