Before anything, I only used LibreOffice once or twice so I'm nowhere close to an expert on that software, therefore this answer applies to general models, like in your screenshot,
The above being said, I think the approach displayed on your image, is the correct one. The problem here is you seem to be considering the whole software screen as the viewport affected by the scroll bar, which is not true. Whether you consider this problem from a conceptual, physical or programming point of view, edition area is different to any tool bar, no matter where it's positioned. Thus, they have their own set of controls. By doing what you say, not only you'd be effectively breaking Fitt's law, but you'd negate the expected affordance to each viewport. To better explain this, try resizing to a really small window to the point the sidebar doesn't fit entirely, but it needs scrolling. Where would you place the scroll bar for the sidebar if you place the edition viewport's scroll bar in its place?
The point is: edition window is a viewport. Sidebar is another viewport. Top menu is another. And so on. A viewport is limited by its boundaries, and any excess to those boundaries will cause a scroll or overflow that belongs to that viewport AND ONLY TO THAT VIEWPORT. And this is true for most cases: think on a text area: the scrollbar is at the side of the element, not at the side of the page. Same for scrolling areas or frames on a web page, select, dropdowns and anything you could think of (always talking about default behaviors, not novelty approaches or experiments).
Let's take the conceptual aspect: the edition area is a zone that holds no actions other than accepting an input of plain text. Put in other words, this will be the content. However, the sidebar will have actions that affect the content or the canvas holding that content. They don't exist by themselves, but they're bound by content's existence (or lack of it, in which case those actions won't perform anything, because there's nothingto modify).
If you take this to a physical world analogy: let's say you write a letter on a long sheet of paper. As you write, you'll move your hand, and maybe even the sheet of paper. But quite certainly you won't move your desk in order to keep writing down the page. Now, think your desk is your main program's window, your sheet of paper the edition window and your hand the cursor. Your hand moves inside the bounds of the sheet, your sheet inside the bounds of your desk, and even if for some reason you had to move your desk, it will move inside the bounds of your room, but your sheet of paper would remain independent of that move.
In short: if your screenshot is what you perceive as an issue, I'm afraid the behavior displayed on that screenshot is the correct one