There is some merit in limiting who-can-file-for-what, however it also annoys me since it also closes off a route of activism which could help force a consistent application of the rules. (Thus exposing both how bad the system is and also forcing rights-holders to curb their overreach.)
For example, imagine that AcmeCorp lawyers were to abuse takedowns to remove negative reviews of their product, while ignoring positive reviews that are equally-or-more "infringing." Or if multiple companies arranged a kind of ceasefire-cartel while using the law to persecute others. If a citizen could "help" them with removing all that content they "missed"...
Insufficient
But the prerequisite to the above argument is that people have a right to upload to YouTube; we don't, but it would certainly be a better service if its users weren't plagued by false copyright claims.