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He's actually talking about growing maintenance cost on fat desktop. Fat application have a higher maintenance cost because you've got the whole release/update process that's made much easier with web apps.
But sure, you'll still need a "desktop" computer with a web browser to connect to these apps, it's just that instead of using firefox/thunderbird/openoffice/your file browser, most users will use an all-in-one cloud offering (like Google gmail/docs/calendar).
This actually make a LOT of sense for most non-technical entreprise users that usually just use an office suite and some internal apps (that are more and more web-based).
But you'll still need fat client for most resources-heavy apps : programming, cao, photoshop, etc...
I mean it's kind of the same thing as with the commandline interface. In the 80s, it was the only interface everybody used. Now, for 99% of users, it has been replaced with a GUI, but it's still useful for the techies.