James,
That might work to some extent. Although to generalize over my testing system you'd have to walk the DOM and do this to all the scrollable elements. Then there's the issue that this will trigger layouts all over the place, likely disturbing the system under test so much that it might do more harm than good. And I'm not 100% positive, but I believe there are circumstances under which setting the overflow: property can actually disturb the scroll position (even if that's not true for most cases, it certainly is in cases where you have "fighting barely-scrollable x/y scrollbar" situations).
I realize that the WebKit platform layer gets pretty horrifying when it comes to dealing with native controls, and scrolling in particular. But given that it's already become common (on Macs, at least) to not have scrollbars take up any layout space, every platform wants to render scrollbars differently, and no one will interact directly with Phantom-rendered pages, I thought it might be worthwhile to consider not rendering scrollbars at all. There may be other issues I'm not thinking of, but it certainly seems like a simple solution to an otherwise-hairy problem.
Cheers,
joel.