Not having used anything except for Firefox, I don't have any experience with migrating to different browsers. However, my understanding is that Chrome shows a little pop-up that lets you import from previous browsers rather than relying on the user to do a data export. Correct me if I'm wrong about this.

I suspect that Claude couldn't make an "import from ChatGPT" button because OpenAI would make it difficult, so they'd have to rely on user initiative and technical capability (exporting to JSON and importing from JSON is enough technical friction that the average user won't bother).