If you've ever studied literature or storytelling, you've probably heard that the basic element of drama is conflict. There are plenty of ways to create conflict, but popular fiction tends to focus on person vs. person conflict.
The most straightforward way to tell a story is to pit a hero against a villain. In popular franchises, a particular villain tends to stand out as the hero's archnemesis. The film industry in particular tends to force stories into this mold, particularly when adapting other media.
Professor Moriarty is undoubtedly one of the most iconic archenemies in pop culture. Moriarty is one of the only characters who can rival the brilliant Sherlock Holmes. Essentially every adaptation features some version of Moriarty, whether it takes place in the Victorian era, modern day, or the distant future. However, Moriarty only appears in one of Arthur Conan Doyle's original stories. At the time, Doyle wanted to kill Sherlock Holmes, and created Moriarty solely to act as a convincing threat for the final story. Most adaptations drastically increase Moriarty's role, making him a lifelong adversary rather than the capstone of Holmes' career.
A very similar thing has happened with the Teenage Mutant Ninja Turtles. They've faced the Shredder in almost every cartoon, video game, and movie (we're not counting the time travel one, for obvious reasons) they've ever appeared in. In the original comics, however, Shredder is dispatched at the end of the first issue, having been stabbed, knocked off a building, and blown up. Side note: the Ninja Turtles weren't entirely kid friendly in those days. He's returned a few times over the years, but he's hardly the constant presence he's been made into in other media.
These may be the most pronounced cases of archenemies taking precedence in adaptations, but there are certainly other examples. A quick glance at this wikipedia entry shows just how many villains Superman has faced over the years, and yet all but two of his live action films have featured Lex Luthor as a major antagonist. The dynamic between these two characters has worked for decades, but that doesn't mean it needs to be the focus of every Superman movie.
There's nothing wrong with archenemies as a concept. Having a personal, longstanding conflict with the hero can bring some welcome drama to a story. However, it's not the only way to create conflict. Sherlock Holmes works just fine without Moriarty, and sometimes Superman needs a break from Lex Luthor. These kinds of characters have expansive histories to draw from, and adaptations lose a lot of welcome variety by having such a narrow focus.
There are countless variations on the archnemesis concept, and plenty of ways to make it compelling. However, not every story needs an archnemesis, or even a villain. It's good to have variety within this type of story, but it's also good to have stories outside this type entirely.
