The whole point in multi-signature scheme is to remove need to trust Coinbase. Your local client and local wallet are fine, until your keys are stolen by malwa

The whole point in multi-signature scheme is to remove need to trust Coinbase. Your local client and local wallet are fine, until your keys are stolen by malware. Multisig scheme also attempts to fix that flaw. EDIT: multisig scheme with user's key on Trezor. This way you are also protected fully from viruses stealing your local key.