I agree. In addition to the concerns you brought up, I see other issues with Pike's proposal. If computers are infrastructure, I'm forced to deal with whatever computers others have. This is a problem, because most people don't use computers as much as me and aren't willing to spend as much on them. I'd rather carry a maxed-out 11" Air everywhere than put up with my friends' and relatives' computers. (In fact, I do this.)
Pike doesn't address security either. Would you log into Gmail on a public computer? Would you enter your credit card info or visit your bank's website? I sure wouldn't. Phones from 20 years ago didn't have any storage or computational abilities, so these security concerns didn't exist for them.
While I'm a huge fan of cloud-based storage and synchronization, there are just too many issues with using untrusted computers everywhere I go. Maybe it was due to the interview format, but I'm surprised such an intelligent, technical thinker managed to avoid discussing the downsides of his proposal.