I'm not saying this can't be fixed, but please remember that this design is responsive, at least partially to cater to users on screens that are smaller. Moving that content up is a solution but it makes it so that the page can't collapse as much before losing the right sidebar. On top of that, we'd lose some page consistency, which is usually a good thing. Below are some illustrations of this, using MSO as an example.
Here's the site's minimum page width with both sidebars:
As you can see, there's not sufficient room between "Top Questions" and "Ask Question" to fit the four tabs "active", "hot", "week", "month".
Collapsing further than this shoves the right sidebar to the bottom of the page... which is (I'm guessing) why the "Ask Question" button isn't in the right sidebar any more.
Here's what the page looks like when it's just a touch narrower:
If you test this yourself, you'll find the entire right sidebar is hanging out between the page content and the footer.
If a solution can be found that still allows users the full site content - both left and right sidebars and the main page content - that'd be great but I do understand why they made the decision they did about the placement of these tabs.
This gets even more complicated when you're on search results pages, which add the number of results next to the tabs, more tabs, and longer text than "Top Questions".
For example, here's a tag search result for stackoverflow-for-teams:
And, at the narrower page width, this still looks really nice and full, as the long search header wraps to a second line along with the "questions" text moving below the quantity of results:
So, for consistency between the different pages, I'm not actually sure there's a better solution. Yes, it does look a bit barren on the Top Questions page at wider views but everywhere else it looks good with just enough white space to separate the areas of the header.