None of the cons of website actually need to be cons, they dont need to be slow, they dont need to have unsuitable UI's for mobile, and they dont need to break when they go offline.
We have done a bad job up until now of realising users expectations that the web should have a great / simple ui and work offline, we just need to improve, much in the same way as the slow transition from desktop apps to web apps has been going, I think its inevitable that we will build most of our technology for the web
I think he forgot to take into account the mobile version of websites, which can be just as simple as native apps, and almost as fast (since they don't have to do much anyway).
> I think its inevitable that we will build most of our
> technology for the web
If by that you mean connected, then yes. If by that you mean "using HTML, CSS and JavaScript"—not necessarily.
As someone else mentioned in comments the most likely scenario would be backend with API and native apps and web apps as clients for that API.
We have done a bad job up until now of realising users expectations that the web should have a great / simple ui and work offline, we just need to improve, much in the same way as the slow transition from desktop apps to web apps has been going, I think its inevitable that we will build most of our technology for the web