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I think the problem is that you have no iOS experience. Those "bubbled" numbers are called (notification) badges, the informational messages that appear at the top of the screen are called notifications and can also be found in the notification center. IIRC it's the same with Android. Well, Android borrowed the badges, iOS borrowed the notifications.
Personally I don't think these feature should cause any confusing, certainly not on the long term and users prefer to have them.
Neither the badges or the notifications change the icon grid in such a way that people are not able to launch their favorite apps.
You must have A LOT of apps you use regularly if you can't fit them all on one page. On my iPhone I have only 3 screens: the home screen which I left mostly like Apple made it, one screen with all my serious apps and one with games. In total I have 197 apps, which is far more than I would gave guess to be honest. I can't imagine you having so many regular apps that they wouldn't fit on one screen.
All my social apps are in the bar at the bottom in a folder, mail is at the bottom too. This is where most badges appear so they are always in sight.