Here's an idea: a card with a magnetic strip on each of its 4 (or 6 or 8) edges. Now instead of carrying multiple cards you carry just one. If you use both sides of the card, you could fit 16 mag strips on an octagonal card.
Here in my country, banks make a large profit out of fraud, albeit indirectly. They offer fraud insurance. They purchase the insurance from someone else for about USD 1/month, and sell it to you for USD 6/month. Of course most people never get to claim anything. Each time there's anything related to credit card fraud on the news, banks get more people buying their insurance (here banks are the only credit card-issuing institutions). If banks offered a cheaper/free way to reduce or eliminate fraud, they would also kill their insurance business.
About the multiple strips cards: In Japan they're already using NFC cards with internal chips that can store several different cards information. The info is encrypted so that only certain authorized card readers may read corresponding card info. Checkout: http://www.sony.net/Products/felica/ http://en.wikipedia.org/wiki/FeliCa