Yeah, I wondered about replacing the cable from ETP to modem, but how do you fit CAT6 cable to the phone jack style connector in the back of the modem? .. or do you mean just to the wall socket?
From the ETP to a wall socket, though the Fritz has an RJ45 on the input so wall socket to modem is also cat6. In my case it's actually ETP->cat6->19" patch panel->patch cable->19" patch panel->cat6->RJ45 cat6 wall socket->cat6->modem. I'm very close to the cabinet though (100m), for a more marginal connection it might be worth trying to avoid so many connectors.
Your Fritz must be different than mine, I don't have an RJ45 for the SDL line in to the modem, only a smaller analog style phone plug socket ... (my FritzBox is a 7490) ..