I don't think it's a tenuous link at all. The link between Bilbo and Frodo is a huge part of the story, an essential part of the history of the ring, how and why it gets passed down, the link with Gollum, Sting, the Mithril shirt and so on.
Yes, I can see the filmmakers using Drogo for some other reason, but not to use him to show exactly how Frodo became Bilbo's heir, having introduced Frodo's father, seems a bit far fetched.
When I said that part of the bridge movie could still be told, I'm not suggesting hours of it, a massive amount could be shown in a very few minutes. I think we will see that.