Since I invariably use my phone many times throughout the day, I really don't see how the above example provides any added benefit. Especially since it only applies if you aren't in viewing distance of your phone at the time of notification.
So you know if you have a missed notification without touching the phone. What do you do next? Do you know if its important? Do you ignore it? Do you pick up the phone and check it? The ability to look at my phone without touching it and generally know if I have something waiting offers no benefit to me.
I can pick up my phone - as I normally do throughout the day and with one tap of the home button I see EXACTLY what I've missed. I know what's important and what to act on.
My phones spend most of the day on my desk at work. Notification comes in, I glance down and see EXACTLY what it is. I know if its a text from a buddy telling me to come down to Houston for the weekend or if its a text from my wife telling me something far more important (because everything from my wife is far more important than anything else

).
I'm a tad confused by this. First, if you open an app with a notification and act of whatever the notification is, it DOES clear in the drop down menu.
Second, I hated those persistent icons in the menu bar. Cluttered looking and served no real purpose. iOS does provide colored banners with information for specific apps that are running (maps, phone, facetime) but other than that, what real purpose does keeping the twitter logo in my menu bar serve?
Days? Really? You run into this situation a lot where you have DAYS of notifications waiting? Again, the notification center DOES clear when you've acted on said notification. Not sure where you're getting your info from....
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Nope, just someone who thinks the notification light is overrated and thinks some of the phrases used here are a bit over the top.
Just presenting my views on why I don't see any real benefit to one. Again - Apple can knock themselves out adding it. I couldn't care less. But I've seen people hail that little light as "game changing" if it were added to an iPhone....
Really? Game changing? I think people have a pretty low bar set if a notification light is game changing. Makes me wonder how much they really know about the iPhone.
And I did turn it off on all my Android phones. Kept hearing how amazing and life-changing it was so I tried it for a while. Even downloaded an app for extra customization. Didn't last long.