What are those 7 languages, anyway? The guy has a strong point he can make without exaggerating. If you want to capture > 90% of the mobile market, I think you only need Objective C and Java.
If you want the rest of the smart phone market, you'll need a C++/QT app, another Java app, and a .Net app. Conveniently, you can #include lua.h in all of these (except maybe BlackBerry) and end up only writing the UI code in the native language.
The performance isn't an issue, but Google Docs still isn't anywhere near the quality of Keynote or Word. iCloud will remove the advantage of instant synchronization, so there aren't many upsides (as a user) to avoiding the native app that adheres to your platform's interface guidelines.
Web apps were a natural bridge into the "cloud" world but now that we've all gotten good at decoupling our UIs from our backend and building all our web apps like a service native apps can just as easily be natural clients of the cloud.
Ultimately, whoever writes the checks gets to decide what to strive for. If you can afford to hire a developer for each platform, great. Otherwise HTML5 is a compelling alternative.
Write once, run anywhere. Why didn't anyone think of this before?