There are big privacy issues to getting data from browsers. A lot of websites depend on "secret" URLs, even though that's unsafe, and we don't want to discover or archive those. That means we need opt-in, and smarts.
We do have a project underway with major browsers to send 404s to us to see if we have the page... and offering to take the user to the Wayback if we do.
More and more people are starting to rely on "archive.is" as it handles Web 2.0 content without issue. But I'm concerned about the survivability of that survice, and whether it can handle big growth.
I call APIs like this "accidental APIs"! From looking at our traffic, we have quite a few programmatic users of it.