I'm not sure about US or European banking, but in Australia we have three methods that work like this - BPay, direct deposit and cash/cheque. BPay is a company that sits in the middle and is, I gather, not financially viable for smaller companies, a direct deposit can take days to appear, and cash is not that great for online transactions.
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
I hate that I cannot lock/unlock my credit card (online wire transfers, checks or other payment methods) at will, with a simple click of my mouse.
I'd really like being able to choose when my credit card can be used, maybe using rules like: "only on weekends, between 11am and 7pm. never online.". Then if these rules are not met, no payment should be authorized. Alternatively, I should be able to have more lax rules like: (all the above) "And only with automatic phone confirmation on weekdays between 12pm and 2pm". Then if I needed to pay for lunch, I could do so with my credit card, but authorization would be granted only after I got an automatic call with a recording asking me to confirm payment and maybe enter a pin number.