Sure, eventually, however I'd be just as comfortable using a plugin from, say, the EFF as I would having it built into the browser. It would be a fine stepping-stone (similar to how Google Gears contained many features which influenced HTML5)

And as I mentioned, merely having the crypto parts and key management built into the browser isn't good enough because a malicious site could still trick you into decrypting data which it could then steal, even if the keys themselves are perfectly safe.