It's my understanding that the EU right to be forgotten legislation places the onus on the search engines to do the delinking. It's the search engines that have forms to submit requests to, not BBC, CNN and so on. It's the search that provides the visibility.

I've no idea if they considered barrier to entry or relative size when drafting the law or built in any limitations. Of course until an engine reaches some level of popularity it's unlikely to receive many or any removal requests, so should remain manageable for them. If it were the individual sites every site would need a policy and takedown request, just like most have now added something for DMCA requests. Doesn't that just put the barrier to entry up for everyone publishing a site?