Personally, I think the Dashboard concept needs to be completely rethought. Not only thinking about how the current implementation can be improved, but also what is the Dashboard really supposed to accomplish?

Yeah, I agree. What is the dashboard really supposed to accomplish? I'd say this is what I would expect it to do for me as an administrator:

The more I think about it, the more I’d like to see the Dashboard function just like the Dashboard in my car. Give me warnings or caution signs of things that don’t seem right such as a page or link that is causing 404 errors for people, the average page load on the site increasing to an unacceptable level, etc.

But that's for me as an administrator. After all, as an administrator, I'm the one driving the car. But that kind of dashboard wouldn't be very useful to non-admins. I guess maybe they really don't need that kind of dashboard - and maybe some of the lower roles don't need a dashboard at all. So I think giving different roles different landing pages makes sense. But it would really depend on the nature of the site - for some sites the dashboard might be really important at all levels. So I guess it comes back around to how can the dashboard be made more useful and more customizable.