But the burden of proof on what? That my opinion is that there are centralized mixers that accept the trade-offs of being centralized/be a trusted-third-party to do what their service is supposed to do?

¯\_(ツ)_/¯

Because I didn't accuse centralized mixers and centralized coordinators for not doing their jobs, although I understand that it's possible for some of them to be operated by bad actors.