Even if the data is encrypted, if the (again, open source) browser can display it unencrypted, it can save it.
Then I began thinking the implications of this. I see a couple of options to enforce this. First is to restrict my operating systems so that I just can't do some things with it, like, well, compile the browser. This is of course hard, because I could use an open source operating system, and if I control my computer, I can bypass things like this. I don't think the content providers will get the access to administer our computers, though for example Blizzard seems to do that in some extent.
Secondly, and this is the more realistic and annoying option: the content on the WWW can move from text-format HTML, CSS and scripts to proprietary binary content. This would mean encrypted formats with no publicly available specification. The data would then be displayed using binary browser plugins. I see a lot of problems with this, beginning with the fact that the users of operating systems other than Windows or OS X, or probably Android, would be left without the content. An another problem is that the user's computer would need to run this binary blob, and therefore it could be disassembled and implemented anew. Version handling and updating the binary blobs would also be a pain.
So, I can't see a working method for implementing this. Either it just doesn't work (os browser) or it will just recreate the Flash problems in a much larger scale. Also it might also mean dividing the Web into multiple parts with different standards and closed binaries.
I don't see how anybody would benefit from this, except again the companies writing and selling the DRM software. Somebody will anyway decipher the encryption and share the protected content.
I'm eager to hear other ways to implement such controls - especially if they work around the "compile your own modified browser" problem which seems to be inherent to this.