How is the web stable? Any server can change the app you're working on without you being able to do anything. Tons of the old web is broken or gone.
Compare that to a win32 desktop app that will almost certainly keep working indefinitely without any changes. Plus you can use proper files for storage.
I was talking about web as technology stack. The tech is battle proven and capable. I had great success in getting some ancient web projects to run locally, less luck with Windows projects and even less with Linux sources.
You are right that by the nature of web the long term stability is not guaranteed. The ecosystem could do more to encourage decoupling and graceful degradation. About 95% of modern web is competing in sharing your data to even more "parties with legitimate interest".