The 2 biggest problems with bitcoin right now, affecting its growth, are security (which is being addressed) and difficulty of use. Most people do not want to download a client. It is a hassle. Bitcoin.org should let people get an address, send/receive payments. Get them to register with an e-mail address. Build a list and start marketing bitcoin like you would a business. For bitcoin to be successful, it needs to be easy. Not everyone will participate in the p2p, but they need to be involved in the bitcoin economy. I will let IT people chime in with the technical requirements for this.
There are already several webwallet providers that provide exactly this service. I believe they are also mentioned in various places in the wiki. I don't think that, for the sake of decentralization, it would be a good idea for bitcoin.org to run a web wallet service.I know there's a psychological barrier involved in downloading the client, but from an ease of use perspective Bitcoin is not any more difficult to get started with than any other software package. It's literally install and go.
I agree, but the psychological barrier is an insurmountable barrier for many people and will restrict the adoption of bitcoin. I would like to see more marketing from the existing web wallet services you mention.
I understand where you're coming from, but consider this...say you are traveling and need to access your money at an internet cafe. How do you do it? I think the client has limitations. For growth, I think the key thing is bitcoin is as easy to use as possible.
There is always the risk of a wallet stealer running on an internet cafe computer, but then again - there's also a risk of a software or even hardware keylogger being present!