I'm assuming there's multiple authorization steps including your email, which should be encrypted - like protonmail,

2FA authenticator like authy or Google authenticator.

Maybe there's a tradeoff without giving up your identity,

Although the benefit doesn't make sense to me - if they're holding your coordinator file and a key then yes your identity matters.

But, if they're holding only a key and no coordinator file, then even if they have your identity they can't tie it to your Bitcoins as the addresses you're using are unknown.