Sometimes I'd like to have control over my full page representation and width across browsers and OSes, and scrollbars styling is missing or non-uniform or unreliable.
EDIT: Scrollbars are inside viewport, meaning they're effectively part of my document, and I'd like to have a say how they look like, the same as form elements.
Ugh, no. I want every UI control to look the same, everywhere. The scrollbars are not effectively a part of your document. That's not the case for a browser, or an office app, or anything that displays scrolling content. They're a property of the container, not the document.
Funny, I just replied to TheZenPsycho and mentioned in an aside that I recall older IE versions (and possibly recent ones as well) did allow the content author to apply styles to the scrollbar with CSS. I have had mixed feelings about that but in general, I would agree with you that it should be open to styling.
I agree because I assume the scrollbar would retain its functionality. By styling it, I don't lose, for example, individual adjustment buttons at each extreme, drag to scroll, and paging by clicking the empty space on a Windows PC.
On the other hand, if I style it, I'd probably want to do so in a context-sensitive manner, applying a specific look for mouse-enabled contexts and another for touch-enabled contexts. And then I end up have to make the same decisions Apple and Microsoft have had to. :)
Not just IE; Webkit allows absurdly extensive CSS customization of the scrollbar. You can see it in action on Google+, or an overview of the features here:
EDIT: Scrollbars are inside viewport, meaning they're effectively part of my document, and I'd like to have a say how they look like, the same as form elements.