I am sorry, but this is BS. This charitable idea unfortunately rests on the false premise that Internet works the same way as press does (and thus one can control and censor it using the same means).
This is not about kids being drunk and getting a photo of them sleeping in a garbage bin posted on some news website - that sort of stuff will pretty much disappear after few years by itself, because it is expensive to maintain all this crap accessible and its publicity value has been zero few hours after it was published already
The larger problem is that a lot of information that is public in common interest gets suppressed - e.g. why a crook should have the information about their crime removed only because they feel like it? E.g. here in Europe it is common that for many jobs you have to bring a copy of your criminal record showing that you haven't been convicted. Expunging something from there typically takes an act of court and many years (typically only after 10-20 years after the sentence has been completed you can ask the court to expunge it). If a kid was stupid and landed in jail, having their crime removed from Google will help them exactly zilch. Then you have people who want to have information about them suppressed for vanity or political reasons - that is straight censorship and there is little reason why that should be allowed.
The search engines shouldn't be (and cannot be) the ones shouldering the burden of whether some of these requests should or shouldn't be allowed. They don't have the resources to judge whether or not the request is valid and they have a conflict of interest as well - it is pretty much to be expected that they will simply remove stuff by default in order to reduce the hassle and avoid having to go through courts (why would they - it would be only a net loss for them either way, even if they won it). So in the most cases the public interest just flies out of the window. .
Finally, this approach of how to achieve the goals of removing the information is completely bogus - basically it is like court-mandated sticking head in the sand so that you don't see the problem. That you stick the head in the sand doesn't mean that the problem ceases to exist - the fact that Google or Bing stop listing the information doesn't mean that the original website that has actually hosted the information pulls it down as well. So nothing has been actually "forgotten" and it only takes a search on something like Yandex or some other search engine that doesn't care about these requests (e.g. BBC) to uncover it again. I am pretty sure that sensation-hungry tabloids will be using this to fish out juicy dirt in the future. So what has been achieved apart from spending millions on a bogus remedy here? Andersen's Emperor's New Clothes comes to mind here - it only takes one person to yell that the emperor is naked