Just because the payment processor is using some of his own capital to make transactions efficient does not mean that there needs to be a credit relationship between he and his customers.
I'm having trouble understanding your explanations now. They seem to be more convoluted and vague than they need to be.
A credit relationship exists as soon as a customer deposits BTC with the bank, and is given demand deposits in exchange. The demand deposits are credit, that others accept as BTC, because they trust the bank to be good for them.
Not exactly.
When a person deposits money in any modern bank account, the money both legally and in practice belongs to the bank. They have a debt to repay to you. This is not a big deal...it fails catastrophically only once every few generations and is not a major beef I have with banks. But anyway...
Let me first clarify, as my terminology might be unclear/confusing. I'm referring to "bank credit" not as credit extended by the BTC-bank to the consumer, but in the context of credit as a 'claim on an asset', instead of the actual asset. In other words, these promises to pay BTC on demand is what I'm referring to as 'bank credit', and this trust the customer puts in the BTC-bank to pay them back in BTC when they demand it is the 'credit relationship' I'm referring to.
I see a Bitcoin economy reliant on these promissory notes, because a 1 MB block size limit pushed transaction fees to $20, as a perversion of the original promise of Bitcoin. I think relying on BTC-banks and clearing houses to transfer claims on BTC, rather than BTC itself, would take a sledgehammer to Bitcoin entrepreneurship.
My website btctip.com is a good example of an amateur startup that couldn't operate in this high-powered expensive BTC world. On a very active week, I have maybe $20 worth of transactions into/out-of my site. Without low-cost network transactions, these tiny deposits and withdrawals would not be possible.
Instead I would have to accept BTC-credit (promissory notes). In order for my users to deposit BTC-credit into my site, I would have to become a client of a BTC-bank, and my customers would have to have accounts with the same BTC-bank, or a BTC-bank with a credit relationship with my bank, allowing for migration of BTC-credit between accounts on the two banks. This would be difficult, and would probably only give me access to a small percentage of BTC users, rather than all of them, as I have now.
My ability to allow my users to withdraw would likewise be limited to the banks I can manage to connect with.
I would not develop a site in an economy like this, because there would be too many obstacles, my market would be too small, and my disadvantage relative to big players too big.
Say you wish to make a payment to Bob. You can tell the processor, "you know that blob I gave you the other day? I want you to turn some of it into value and give it to Bob." The payment processor looks around and say, "I found Bob. Sign this note which will allow me to give some of it to Bob." I say OK. Moments later, Bob has some value in his account.
This is a substantively different relationship than I have with my bank, and made possible with advances in technology which the banking system has not caught up with.
You're talking about advances in banking, not in Bitcoin. These same technologies could be used in fiat banking, since they're just transfers of claims, that could be for any asset.
To claim that you're going to develop the technology of modern banking so that a Bitcoin-economy reliant on banks is as easy and seamless as one reliant on nodes is pie in the sky idealism that should not be a factor in deciding what to do with the block size limit.