I'm busy too - full time job + overtime, wife, and a new baby. But I can certainly find the time to install a browser and a messaging app on my phone. If you can't find the time to install a couple apps, why do you have a smartphone in the first place? I'm SURE you could find a third-party app to your liking. You don't need to do anything complicated to solve these problems.
Anyway, I hear this reasoning from people who want to stick with ios all the time. The "it just works" reasoning. Unfortunately, "it just works" often means "there is no way to fix it besides waiting a year for the new version of ios, so I'll just deal with it." It's your opinion and you're the one who has to use the phone, so pick the one you like more. But my experience as a former, long-time ios user is that I will eventually find plenty of annoyances with the first party apps (ie the messaging app and safari), and then I won't be able to do anything about those annoyances without jailbreaking or something similarly inconvenient.
I truly hope you enjoy your phone, and I'm not kidding about that. But please make sure it's really the right phone for you and that you're not just trying to convince yourself iphone 5 was the right decision because, from an outside perspective, the arguments you posted are just not that strong.