We'll still need several GB or TB of local storage, be 
  it spinning disks, SSDs or permanent RAM.

Yes I should have clarified -- I expect memristors to be on the market within a few years. Once they're ready I bet we'll see all laptops and mobile devices move over to them. Between memristor based local storage/cache, and large/cheap cloud storage, I don't see much reason for having hard disks, software, and data in our local computers for very long. Just keep all your data and apps on the cloud, and use web-based apps for accessing them. The foundation for this type of computing world is absolutely being built right now by thousands of companies. It's definitely coming.