This prediction is plausible based on the trend to vendor-managed devices amongst the general public. However, all the vendors of such devices need GPC's to make them. And certain big industries (incl. financial, pharmacos) won't tolerate not having root. So GPCs will continue being manufactured and available in the market, though they might become expensive or regulated.
There are factors to consider in addition to the popularity of iDevices, tablets and such:
2. Will there or can there be a non-GPC that is usable for software creation. It is certainly possible for creation of text, images and so on, and some solution that allows using a managed language to produce binaries could be locked down fairly well. Certainly the likes of Microsoft and Apple would promote this, and the dot-net ecosystem already approaches it.
3. A possible dystopian scheme where the government tries to control access to GPCs and allows coding only on "captive" PCs as per (2).
4. Developers being discontented with (2) enough to reject the share-cropping arrangement and create a market for GPCs for individuals.
5. General public discovering advantages of having root on their gadgets and creating market demand, even though they will have little idea of the details ("I can do X with it this way but not when it's subject to the telco")
It's true that kids today won't experience computing as a revelation to the degree we did in the 80s.
I don't think that matters all that much, though. Cameras were invented a long time ago, but plenty of kids still get inspired to pick one up and learn how to make compelling images...same with music, film, writing, painting, sculpture, etc.
All kids today need are the means to learn (it's never been easier) and a reason to give it a try (there millions of games, apps, websites, etc. to inspire them).
Fair enough, let me rephrase it: he is parroting a common cliché, one that is based more on the desires and trends of the contemporary computer industry than a deep reflection on the future of humanity.