Yes, but it speaks to the “if the problem is more on Russia firing many more missiles” bit that you raised. I suspect that it’s probably more-practical to dramatically reduce Russia’s access to a continued supply of ballistic missiles than to dramatically reduce Ukraine’s access to a continued supply of ballistic missile interceptors.
That’s a discussion far beyond the scope of “Is the Patriot in its existing configuration working as needed?”
Yes, but it speaks to the “if the problem is more on Russia firing many more missiles” bit that you raised. I suspect that it’s probably more-practical to dramatically reduce Russia’s access to a continued supply of ballistic missiles than to dramatically reduce Ukraine’s access to a continued supply of ballistic missile interceptors.