Cut-thru payments
A future version of the payment protocol can allow the receiver to give the sender a BIP32 seed, and a total amount requested value. The receiver then considers the payment satisfied once outputs with addresses derived from that seed exist in the blockchain with a total value >= the total amount requested.
This means a merchant with debts to someone else, like their employees or suppliers, can get PaymentRequests from whomever they are in debt to and in effect have their customers pay those debts directly.
If those suppliers in turn have debts to other parties the process can repeat again. This time the supplier to the merchant just gives the merchant a list of addresses to pay, addresses that happen to belong to whomever the supplier owes a debt too. (maybe their employees?) Now two steps in the whole payment process have been skipped, and the customers of the merchant could very well be actually paying into wallets owned by employees of the merchant's suppliers!
In the business world 'Net 30 days' accounts are very commonly used, so this kind of arrangement could actually be quite practical and useful. Everyone in between saves on transactions fees, there would be a lot less demand for blockchain space, and privacy is improved for everyone.
Of course, it'd be a bit surprising if you went to pay a bill on Thursday night and the moment you paid it your wallet told you your employer had paid the exact same amount as part of your upcoming Friday paycheck...
I don't understand how come the debt creep into the picture? Bitcoin is a payment system, but it seems these are some accounting function, more like a clearing house. But shouldn't the settlement be handled off-chain by some bitcoin clearing house, and all the merchants have business relationship in one area connect to this clearing house instead?
Debt crept into the picture because the parties in it agreed too. Note how what I'm describing is much more organic than any centralized clearing house: it's just showing how what businesses do routinely - extend 30 day credit relationships to each other - can turn into a way for them to organically, indeed, accidentally, create something akin to the Ripple network with the help of suitable accounting/wallet software. Note how that as long as everyone involved has
some mechanism to tell a third party "pay me these amounts at these addresses to settle our debt", and accounting/wallet software keeping track of the payments as they happen, the result can be a cut-thru payment system. The parties
don't have to use the same software, or for that matter the "official Payment Protocol", and in fact in theory everyone involved could be doing it all manually.
I'm concerned about the block size limit
Yes you should be. Notice how all of the above would have never happened if transactions are free or nearly free - why bother? Instead every step would be just done with individual transactions; certainly easier but the cost is a centralized system with bandwidth and storage requirements that only a select few miners can keep up with, and importantly, afford to audit fully. Or in the words of core developer Jeff Garzik:
(g.2) Competition for space encourages efficient solutions, whereas a too-loose block size policy incentivizes the opposite: dumping into the block chain
[...]
And very importantly, (i) it is a mistake to increase block size simply because people are too lazy to implement layers on top of bitcoin. Bitcoin will forever be a zen balance of applications and layers that sit on top of the blockchain, and those that directly use the blockchain itself as their comm/functional layer (c.f. SatoshiDICE).
-http://garzikrants.blogspot.ca/2013/02/bitcoin-block-size-thoughts.html
Mike's post on the consequences of centralized mining is interesting too:
Freezing BitCoin addresses by regulating miners