It might be better if email clients have the CC field disabled/hidden by default, and for mail servers to strip out that field from external emails.
Considering you have just described exactly how the BCC header works, why would you filter out the CC field? If you don't want it stripped out from recipients, you use CC, if you do want it stripped you use BCC. Although having a warning pop up in the client when sending external emails with a lot of CC's, an "All recipients on the CC list can see the complete list of CC email addresses, are you sure?" is a thing and can be done on enterprise-grade email clients, outlook, lotus notes (does anyone still use this?).
Better still, when sending corporate communications mass-mailings, don't fire up your standard email client, use one of the numerous 'email-merge' programs, where you write a form email, have a list of recipients, and the app will take care of sending the emails by generating a separate unique 'personalised' email for each and every recipient on the list.