Nah, I hate that. Frequently it gets in my way when I have my screen split with two browsers side by side. I'll try to hover over the scrollbar on the right hand side of the left page, try to click, and end up clicking the right window. Give me the whole damn scrollbar please.
Yeah, if I'm reading something, I want to have an indication of how long a page is and where I am currently. I don't want to have to move my mouse somewhere to get that information.
Then the only way to scroll on desktop is to highlight text across the frame's edge.