Don't get me wrong, I'm not advocating this principle or implying it is needed and doable with the current technologies (I don't think we have a way of reliably storing such long-term data within the user's browser), but it's an interesting train of thought. It doesn't obviate the need for the server to store any sensitive information, just some of it. User info, password hashes, credit card numbers, maybe even social graphs depending on the use case, could all be stored this way. There will always be websites for which this doesn't make a lot of sense, but a lot of the other ones, mainly small players, could benefit from this.
It's curious how, when you describe it like that, it sounds that your data is being held hostage by a third party. After all, the server doesn't allow you to see what's in the encrypted opaque blobs, it only allows a controlled set of operations to be done with this data, and the only thing they do is further mutate this opaque blob. But it is no less transparent than the current state of affairs, namely servers keeping the data for themselves.
I'm interested to hear HN's opinion on this, flaws in the approach I've missed, etc.