The problem is most third-party iPad apps continue to store their files in their own internal sandbox. You can import from and export to the Files app, but working files are stored in the sandbox and therefore not accessible from Files, only from within the app.
Apple's own first party apps like Pages, Numbers, and Keynote do this properly; when you open them they bring up the equivalent of an Open/Save dialog from Files and you can save the files wherever you want. Microsoft Office has gotten slightly better at this but still uses a custom interface. But if I want to open a file from Photoshop, ProCreate, Affinity, or any similar app I have to use the in-app interface and whatever organizational tools I'm given.
That's not anything Apple can fix, that's on the app developer to use the tools they've been given.