Sure, I do. And it doesn't seem that people that still have to support Internet Explorer have a much easier time considering that they seem to have settled on using a whole additional layer of abstraction !
It really comes down to ease-of-updates. Web apps are trivial to update. No build / cross-platform / deployment issues that you encounter with native apps.
Velocity of updates is also important. If I update a package, it can take weeks, months... maybe years... before end users update. If I update a web site, it's instantaneous.