It is actually much more convenient for users. They can switch computers/phone/OSes and have the same experience. The same is not true with native apps.
I don’t want the same experience cross platforms. I don’t want the “Mac experience” when I am using Windows (see iTunes) or the “Windows experience” when I am using a Mac (old versions of Office).
No, what you want is the same experience. Which is what the web gives you. What you are describing is native apps trying to replicate the same experience and failing because they are native.
Edit: Native apps require more maintenance which adds to the delta in experience. If a single app is created (web) there is no delta.
It's more convenient for some applications, but it's not the case yet for many applications. Evolution of browsers will probably favour web platform for everything except the more close-to-the-metal ones.
