(For myself, I don't see why this is a problem. DS9 and Voyager didn't recycle characters from TNG outside of a handful. There's a lot to be said for doing something original in the universe so it has its own voice.)
I agree mainly with your analysis but wanted to address this. The advantage that Star Trek has through all of its TV series is that it is one cohesive universe that has an established history, politics, alien species, etc. It's more akin to a real but distinct universe. Really, DW's strength is that it can go anywhere and do anything but it doesn't really have a distinct universe it can claim as its own. It has distinct aliens, villains, etc. But, they seem to show up in a random assortment of places for one off conflicts rather than an ongoing conflict with context and history, say like with Cardassians, Klingons, Romulans.
So, for a DW spin off, it's not enough to say it's set in the same universe. I think you really need some strong carryover element, particularly characters.
I disagree.
I think the
Doctor Who universe is developed enough and rich enough to be as cohesive as any other fictional universe out there. Just because the Doctor's adventures cross times and genres doesn't mean that you can't place something in the
Whoniverse. You could do something like "
House of Cards in the
Doctor Who universe" (which is what
Children of Earth's "Day Four" basically is) and see how the British government deals with
Who things happening in the background. You could do "
The Hour in the
Doctor Who universe" and see how the media (Trinity Wells, anyone?) covers things like giant eyeballs appearing the sky. Heck, you could even do "
Star Trek in the
Doctor Who universe" set on an exploratory starship from one of the future Human Empires.
All of that said, I would
love an Osgood sitcom with Ingrid Oliver, which I think could be brilliant -- socially awkward genius who works for a government organization and her screwed up social life (like her sister) in London. I'd watch the heck out of that.