What you're describing seems to be a natural process through which people try to cope with the new reality. New social norms are created and enforced to make people avoid one another's past timelines, and market forces emerge to make search engines rank more recent pages higher. It's all part of our natural response to what makes us uncomfortable. We respond in such a way as to restore comfort, because being creepy is neither polite nor profitable.

What that doesn't fix, however, is the fact that old information is still out there, on somebody's server, every bit unchanged and ready to resurface at a moment's notice. Sometimes the old information is just a statistic in the grand scheme of Big Data. Other times, it can be very specific, such as the one-liner that allowed the Feds to attribute to Ross Ulbricht the very first mention of Silk Road on the open Internet.

Computers aren't learning to forget, they still remember everything. We're just training ourselves to pretend that computers are just as forgetful as we are, because it's a comfortable thought. The problem, of course, that collective games of make-believe have a tendency to break down at some point.