Downloading isn't a concern, as websites can already force you to download a file. <img src=...> The new risk is P2P connections that bypass HTTP settings, and perhaps uploading. (You could already upload by making a POST, so it's only in combination with P2P stuff that this is novel.)
If WebRTC prompted or forced use of the HTTP connection settings in the browser, I'd have no issue with it.
That's true but this combination allows for first downloading then serving up illegal content to many consumers and the penalties for that are much harsher. A post would go to one place only (normally speaking) and would not suddenly allow your browser to become server, making you a point of distribution.
So instead of "Someone else did it on my WiFi", people will now say "I didn't transfer those files, a webpage did it without my knowledge". Sounds like a much more solid excuse actually.
If WebRTC prompted or forced use of the HTTP connection settings in the browser, I'd have no issue with it.