...and if you provide online chat with customer support or sales, people will send credit cards in that too. If you have customer accessible support ticket submission system, that will end up with credit cards too.
The Payment Card Industry Data Security Standard (PCI DSS) that you have to agree to follow in order to be allowed to process credit cards requires secure storage of all the cards you store--not just the cards that you intended to store or just cards that come in through channels you intended for receiving cards.
This is a serious issue to take into account when choosing your chat system, ticketing system, and email system because you can't just ignore those wayward credit cards. If you choose systems whose developers did not consider this and failed to provide good tools for finding and redacting unrequested, unwanted sensitive information you will end up having to hack such tools into the system yourself.
1) They don't realise email is not secure
2) When you explain point 1, all of the other solutions seem like too much hassle so they email anyway.
3) You can tell your customers not to email you CC numbers, you can even refuse them, but they will keep sending them