What I mean is that "convergence" benefit is not same UI on different devices out of pure whim, but the ability to use the same application from phone directly

What I mean is that "convergence" benefit is not same UI on different devices out of pure whim, but the ability to use the same application from phone directly or using desktop monitor mouse and keyboard. I don't mean the interfaces should actually be different. Just that "the same interface" is not the motivation by itself. Unified interface would be good for that. If the interfaces are actually different, the app could be adopted automatically by its UI framework, or by "window manager", etc.