interesting, this picture says voip box first
I haven't been following along with the complete discussion, but my provider is Brighthouse and the VOIP box is built into my cable modem. I just connect it to one of my standard phone lines and then all the analog phones in my house are able to dial out.
Now, if you go with a third party device, you can have the topology in your diagram above and also, a topology with the device behind your router in most cases. I believe Ooma supported both scenarios IIRC from my research.