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Well I see several problems with this system, most of which are the reasons it seems Bitcoin is being implemented in the first place.
First off, one question, for you and all of Bitcoin.
Paypal has terms in their Acceptable Use Policy, that states transactions related to "currency exchanges" are forbidden. Is this sort of transaction considered a currency exchange? If so, I see problems arising from exchangers using methods like paypal, just like other e-currencies have problem finding easy funding sources.
Damn, that sucks. That prevents the creation of at least high-profile PayPal exchange services. I'll have to think of some other payment service that can support automation. PayPal would have been the easiest.
I think the program is lightweight enough that anyone can install it quite effectively without any problems. For those who don't want to run a node, they don't have to. Using only the program is even easier and faster than logging into a web account and checking any transactions there.
The idea of a server holding all information and being centralized is exactly what Bitcoin is fighting. Truly, it is unnecessary. I could do a bank transfer everytime I wanted to give my neighbor money, or I could just hand them money out of my pocket. In a sense, a web server would be the bank, and the bitcoin program would be out of pocket. There's no real need for the extra step.
I think you are making much more work for what is already a well implemented program that runs on it's own. Central servers in different countries? 100 one use key orders? You could not even run a node from a web app, so technically all this extra work would only be so you could check your account online.
If anything(which may already be in the works?) bitcoin could be used with your mobile phone to check balances and send them to other members. I never tested this system, but something like
www.opencoin.org has interested me.
I understand the reasons you feel the way you do, but I honestly just feel it's a lot more work that is unnecessary, and it is causing problems in which Bitcoin is trying to solve in the first place.
There's certainly demand on the market for accessing your money from any computer and not having to worry about backups, and I believe web UI's will sooner or later emerge to fill that need when the number of Bitcoin users increases. Centralized access points like the web UI wouldn't threaten the whole decentralized nature of the system. You'd still have the advantages of a stable currency base and anonymous transactions. The service would not be a bank in the sense that they can't borrow the "deposited" coins to anyone, because the "depositor" may still have backups of the coins and use them at any time.
On the other hand, the mobile client is also a great idea and satisfies the need for usability at any location. Backups of the wallet would be necessary though - you don't want to lose all your money when you drop your phone into the ocean or if it just gets broken. One option would be in-built FTP backups (might be too difficult for n00bs though).