Doesn't that require ChipMixer to operate as a bank, and have users exchange those certificates, like money? That's what I understand from the wiki. Here's an even better idea: Lightning. Users hold similar to these certificates (commitment transactions), which they can exchange with the entire lightning network. Not only do they get better privacy (since lightning has more activity than ChipMixer), but the users also maintain self-custody. Alice sends you 1mBTC and gets 1mBTC via LN (the "voucher" essentially). Blinded paths (which are soon to be implemented) can protect Alice from doxxing her public key to you. Once she's ready to spend the chip on-chain, she just sends you the bitcoin via lightning, and takes the chip traditionally.

Good luck on chain analyzing after that.