I'm confused here a tad... besides being annoying because you have to deal with it.. how is this a big problem for people?
If you order something and it doesn't come... call your CC company and contest the charge.
If you find your card has fraudulent charges... call your CC company and report it and you're not liable.
http://www.consumer.ftc.gov/articles/0213-lost-or-stolen-credit-atm-and-debit-cards
Even for Debit Cards (why people use these.. ugh) - you are limited to 0/50/500 depending on when you report it.
No one can steal your identity with just your credit card number and your name.
Certainly dealing with canceling a credit card is annoying while on travel.. but how on earth do these guys make money at this? I guess by not actually making charges themselves... but by selling the card info as middle men so they don't have to worry about things tracing back to them.