Search engines were doing that 20 years ago, before Google even existed. The only thing that has changed is the amount of information that is posted on the web to be indexed — and the amount of time per week the average person spends using the web.
No, there has simultaneously been a huge increase in quality of the search engines (driven by google, to their credit), plus how much of available documents they can search.
Sure, technological advances have allowed search engines to keep pace with the expanding web. But it seems an odd leap to get from there to suddenly blaming them for discoverability* of content.
Besides, I don't think advances like PageRank (the founding technology of Google) are relevant to making old content about a named individual more discoverable.* This kind of quality improvement helps with ranking when you have 100,000 hits. But when you have a unique firstname-lastname combination with 3 hits, all that matters is the number of pages you were able to index.
*Edit: replaced "available" with "discoverable" throughout, per x0x0's critique below, since that was what I meant.
I'm not blaming them for availability, but discoverability, because availability w/o discoverability is, for most people, the same as information not existing. I'm blaming them for massively increasing discoverability, pretending that somehow this is the natural and correct state of affairs (and further, that this is so obvious it doesn't require debate), then pitching a tantrum when a government uses it's ability to control commercial behavior in their country to interfere with what google wants to be the "natural" state of affairs.
is literacy a natural state? If you consider the history of the us, probably just barely.
on to your argument, such as it is: pretending that our two choices are we can have easy access to information or not is, well, dumb: we can certainly allow individuals (as europe has demonstrated) to remove things from google while retaining access to, oh, 99.9998% (first estimate of google's index that popped up on google: 30B pages. removal requests: 70k in 2 months. 1 - 7e4/30e9) of information in the world. And that is a severe underestimate: information can still be returned, just not for particular searches as far as I understand. So starting with humane things like removing revenge porn, whether the host is or is not within us copyright jurisdiction, ad probably moving on to relatively private facts about peoples' lives is a great place to start. I'm not sure where we'll end, but I'm far more comfortable with governments -- who, after all, nominally represent the governed -- deciding than with google.
edit: for another example: particularly the HN audience which runs young, white or asian, male, glibertarian, and tech employee has little to fear from personal info leaking online: sf doesn't care about most things, ranging from lgbtq to bdsm to swinging to whatever. But there's a lot of places that do. You don't have to look far to see what would happen in, say, utah to a high school-aged transgender kid. Restricting that information online is completely reasonable.
Search engines were doing that 20 years ago, before Google even existed. The only thing that has changed is the amount of information that is posted on the web to be indexed — and the amount of time per week the average person spends using the web.