Its also, from a pragmatic standpoint, about equivalent to attempting to command the tides by law.
Except not really. Google, despite what many might like to think, is not an "official" entity, it's a private company. They aren't disseminating information for the public good, whatever that is, but so they can slap an ad on it and make some profits. So what if Jo(e) Bloggs did something embarrassing a decade ago? If one of your friends was constantly bringing up things from years ago, you'd get tired of them doing so pretty quickly. Why should Google get to do it to make some money off of it? And what sort of gossip monger even wants this to be possible?
Before it was varying levels of unprovable (ie, not photographs or verifiable sources) and bandwidth limited (people could only store so much information; sources weren't interlinked for quick queries).
So it's actually quite likely that when we drafted our laws, this was an implicit right by the nature of technology, and considered a natural part of the bounds of specifically enumerated rights.
We should make sure, as technology removes traditional limits on what we can do, that we adequately adjust our laws to reflect that change.
(That said, having links posted on a website about forgotten links is probably way lower impact than having them show up on the first page of a google search for your name. I imagine that most people would be satisfied with this level of obfuscation of their past.)