Discover? I've been a happy customer of theirs since the 90s, and their coverage has gotten near total within the US. Sparser in other countries, though.
With my credit union in California, wire transfers are $20 + 2-3 business days. This is cost prohibitive. Western Union is similarly pricey. Dwolla is an interesting competitor ($3/mo for unlimited instant transfers), but it needs wider adoption before it can be used directly.
In Sweden wire transfers within Sweden[1] generally do not have a per transaction cost and most utility bills are paid through wire transfer. Recently many online stores have started allowing purchase with invoice (many use a company called Klarna[2] which handles the sending of invoices and the risks) which you then have to pay through wire transfer.
1. I think it is usually free to all EU countries too as long as you use IBAN.
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.
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.