So then I'd end up with about 100 "Apps" on my desktop, which all might or might not behave a bit differently,
This is a solved problem... look at how mobile phones do it. It'd be 100x easier on a desktop, since there's more space. Chrome is already doing this -- just add a search box. Easier than typing in a full url, right?
and every time I want to switch to another site, I have to switch the app? How would I follow links outside of the app?
I think this is sort of the point -- people get notified when they're leaving the app. It's easy to follow links out of the app, because the platform for ALL apps is the web browser.
Would there still be a way to find websites/desktopapps? If so, what makes sure that those aren't malware?
Again, solved problem.