It’s fairly impossible to write a story without tropes, which is why some say there isn’t a story that hasn’t been written. Every story, in terms of its tropes, has been told before. Even a classic like Austen’s Pride and Prejudice contains tropes. “Opposites attract”, “enemies to lovers” and “poor girl, rich guy” could all be used to describe its storyline.
So the question is not so much “must my story contain tropes?” but rather “must I begin planning my story with a trope?” The answer to that is no, but writing your story first and identifying its trope later may result in many wasted words if you don’t execute the trope effectively. Identifying the trope from the get-go can provide focus and guide you in meeting your readers’ expectations.
And let me tell you, romance readers expect one very specific trope — a “happily ever after”. Aside from that non-negotiable expectation, tropes in the romance genre abound, and readers often browse titles according to the trope they’re most interested in reading — which is another important reason to identify the tropes in your story. They’re very useful for pitching your story to publishers and marketing it to readers.