How is this relevant? I don't spend much, and use cash in real life. But I need a card for online purchases for my business (hosting, etc.) and for access to my bank accounts in a different country. Maybe I can replace most of it with wire transfer, but Amazon, Rackspace, etc. won't accept it.

You can give Amazon direct access to your checking account: http://www.amazon.com/gp/help/customer/display.html?nodeId=1...

Thanks. It's ACH-enabled U.S. checking account only, so won't work for me, but maybe others will find this useful.

It's a compromise. If VISA and MC bother you in this context, use them less. You can't practically eliminate them, but you can, if you choose, reduce their use.