You don't want to introduce a fee to file takedown notices, as then the people the law was arguably meant to protect (the small content creators) will not be able to make requests as easily, and you don't want to just allow people to abuse the system and use it like a "i want this gone" button.
If I make one thing, and it costs $10 to file a takedown, then the "copyright violators" can bleed me dry by just re-uploading it hundreds or thousands of times.
It's already a massive time sink to make the takedowns, in my opinion adding a monetary cost will just swing the pendulum the complete opposite direction.
It feels odd to price a public legal request like it were a commercial service, but it might be the most fair solution.