Apple is trying to tell you that the web browser is a second class citizen compared to native.

Websites don't need to go through the App Store. No money in that for Apple. Hence, low priority.

the problem is that some native apps are just wrappers for web apps and still fail miserably.

Confirmed on one my sites. Apple needs to give iOS Safari some serious attention, so much has been broken since 7.0 release, especially homepage web apps.

Broken since Beta 4 and they still didn't manage to fix it before release. Apple is seriously asleep at the wheel on Safari iOS.