I've done the email version of card number backups, but not all in one email, I spread it among four accounts (gmail, outlook, hotmail, yahoo), none of which have my name as part of the username. Each account gets a part of the info - 8 digits in one email, the last 4 digits in another, the other 4 and security code in another, month/year in the fourth email. Someone would need to be able to get into all four emails to recreate the number, and if two are compromised, I don't think a hacker could do anything with them. They also wouldn't say "AMEX 12345678", but just be a context-less string of numbers. Yes, it would be more work for me to reassemble the numbers in an emergency, but it feels safer to me.

I do keep an email with all my FF/club/store/hotel loyalty numbers in the body, and another email with important phone numbers, like credit card companies (even for cards/banks I don't use, in case someone else needs it), and I edit it before I travel with the numbers of the airlines and hotels (with addresses) I am using and send it to a family member and trusted friend, in case I can't deal with it as easily. Family member also gets a photocopy of my passport and credit cards (with my itinerary). It almost seems overkill, but I feel it's worth the effort.