You can't backup everything that's on the phone.
Your process sounds great to a technology-enabled person. But for mere humans?
They don't remember their Apple ID password.
They put in random answers to security questions for password recovery.
Their email address has changed, their computer has changed, etc.
They installed all that music, all those videos, and all those apps, like, a *year* ago or more. Who remembers how?
"Can't you just copy everything from my old phone over to my new phone?"
As you say, the process ends up being:
Initialize the phone as new, to their current computer.
Create a new Apple ID and sign them in.
Install and position all the apps one by one by looking at their old phone as you hold it.
Get ahold of all the music that they already bought in some other format so that they don't have to pay for it again.
Give them the bad news about what can't be tracked down/reinstalled (apps no longer in app store, music that can't be found elsewhere without re-buying, etc.)
I could have sworn that in a recent case, we lost all of SMS and she was upset about that, but may I'm remembering incorrectly. Still, the process is onerous.
It pisses people off—"You mean I can't just move all of *my* stuff from my old phone to my new phone? Why do they call it an *upgrade?*"
I'm not saying they're right. Sure, they should remember their passwords, take care of their online identities, etc.
But the fact is that you cannot simply do this:
1. Connect old iPhone to computer
2. Back up full contents
3. Connect new iPhone to computer
4. Restore full contents
I've been on to Apple a couple of times with people standing next to me while I try to act as an intermediary, and the people on the other end of the line end up just throwing their hands up, apologizing, and saying they can't help.
To be fair, this isn't exactly easy on Android either. But it's slightly easier. And both platforms need to seriously work on it.