You can't do this on YouTube because YT satisfied the big copyright manipulators by adding their own system in front of the DMCA. As a result these claims don't go through the DMCA process and the legal penalties (toothless to begin with) built into the DMCA aren't available to you. Content ID killing your content or claiming it because someone misused Content ID isn't a legal matter so you are powerless. This is how it is intended to be: It's what Viacom/Disney/etc wanted and Google gave it to them.

AFAIK DMCA notices only produce a takedown, not monetization. If you want to monetize you go through Content ID, which is not the DMCA.

A false DMCA also exposes you to real legal threat, and a big player with money for a lawyer will dismantle you.