Just to define these terms for our fair readers:
Interchange is the cut that goes to the bank that issued the consumer's card. That is standard and you can see Visa's rates here: http://usa.visa.com/merchants/operations/interchange_rates.h... Processors are the entities that connect merchants to the card network. (These are often also banks, or another org working with a bank.) One of the most important things they do apart from that technical function is vouch for their merchants. They guarantee that consumers are protected from bad behavior on the part of their merchants, like selling counterfeit goods or running tons of fraudulent cards. So that's why it's often a pain to get a merchant account, and why easier-to-get merchant accounts have higher rates (because they have more fraud).
So, yes, processor markup varies. But we don't need a new currency system to drive competition in the processor space. That's orthogonal. That could happen 100% on top of the current system.
So I'm not sure what else you're referring to as "network fees". Visa/Mastercard's slice? Visa's net income last year was $3B, which is not small, but hardly a major share of GDP. There's also decades of worldwide expansion costs (incl. massive marketing spend) that's gone into that.
