If you're talking desktop, I agree, since the browser has become so pre-eminent there. But for mobile, Web apps are distinctly second-tier citizens. Just installing one on your home screen is voodoo beyond the ken of most iPhone users.
It's not so bad on Android. And Google is very good at Web Apps. Try viewing the web app versions of gmail and such on your phone. They're not as full featured as the dedicated apps, but they work damn well. The big thing is making them look like real apps to the end user. No one wants to have to remember a bunch of web addresses. Something like what Chrome does on the PC is good...instead of a classic link shortcut for your desktop, it makes an "app" out of it. Giving it its own icon and name like any other program on the computer.
