You’re right it shouldn’t be the business of a domain registrar. But every provider in the chain that the copyright holders can reach to will end up responsible. You, the registrar, web host, ISP, everything.

Send your complaints to the US government and the copyright lobby. It’s a bullshit law. Namecheap complies with it because if they don’t, THEY get cut off by their own providers, and so on up the chain until the fines roll in.