Is this not already common in certain industries? I've seen plenty of video game terms of service that make you scroll to the bottom before the 'accept' button can be clicked, making all the text at least temporarily visible on the screen. (I recall the World of Warcraft client doing this after every single patch update - no idea if it still does. I'm pretty sure every time I update my PS3 I go through this experience, too.)
I think what rossjudson means is that you're only accepting what's visibile on the screen at the time of clicking accept. So if you scrolled to the bottom, you would only be responsible for the text visible on the screen at the bottom of the page.
I think if the technical details with screen-size and tracking what was indeed visible at the time of acceptance are worked out, that this is a great idea and really would use market forces to naturally shorten TOSs. It has a very Libertarian Paternalism idea about it in that it's not limiting freedom but gives them a Nudge[1] in the more universally beneficial direction.
As a user who just wants to click accept and GTFO, this would initially be a burdon as all existing TOSs are aligned with this requirement. I don't want to accept 60 pages just to install WinRar (the trial of course, because I'm still not sold on it's benefits).
But as someone concerned with what I'm actually agreeing to, and someone who doesn't have the time to read the TOS for everything I come across, I'm fully behind that and would like to have some words with the lazier side of me about the importance of agreements.
As an aside, maybe there could be an article of the law that allows for a legally binding summary of terms which they could use to supplement the full terms. In that case, the user would be bound to the terms of the summary--in reference to the full terms--which were visible on the screen when they accepted. They would still be required to accept the full terms (likely with the same TL;RD scroll and accept).
I'm thinking that there's somewhat of a precedent to such summaries: ballots. When you vote on on a resolution at the ballot, you're reading a summary. But that summary has to be legally accurate to the content of the bill.
That said, one can scroll rather quickly.