In most cases, mobile apps are close enough to web apps in regards to barrier of consumption to make the difference moot, and when you add the native advantage, the result is a net positive consumer experience for mobile apps.
I don't understand why this has to be an either-or thing. I know it's easier for us to think in black and white terms but I don't see why web and native can't coexist for a long time.
How about services that already require you have an account? You have to log into a Twitter or Facebook or Linkedin client even if you install it as a native application.
If all you require to get through the day is an online paint clone, a calculator, a clock/weather app and a game where you throw birds at pigs, more power to you - I'm glad you've been able to shave a few seconds off your day.