I've thought about React Native before, and it is on my radar, but even that feels like a bit too much. I am the sole..everything with renshuu, and with a lovely baby boy that joined by world in January, time is pretty tight!
A native mobile app seems good to have, but as an iOS app developer myself, I can tell you that the effort could consume a lot of your time. Even if you're experienced with Swift, the frameworks, developer tools, etc.
That is of course if you do want to provide a good user experience with offline sync and quizzes, login, and more. I would suggest to improve the web app content, quiz quality, and various other issues that it might have, unless if you do have a lot of free time to focus on the mobile app.
I think you're right on the money with that. I am not proficient with the mobile frameworks, and to be honest, even as a thought exercise, I'm having a really hard time thinking of how to build offline quizzing through the web interface or app when consider just how much data sits in the database that users need access to (personal historical data aside). The dictionaries themselves are not the smallest, but a lot of the vocab/kanji/etc is stored in a lot of different ways to make it easy for searching/validating/etc. when working with quiz answers.