It makes the most sense the way it is and should not be changed.
As others have mentioned, it displays *new* notifications- ones that have popped up since you last checked it. This is consistent with the way the rest of the OS works. If you have looked at the action center and not cleared the notifications, you have obviously made a mental note to address those notifications later and they will still be waiting for you in the action center later.
If the icon is back, something new has happened and it prompts you to look again. If the icon were always there then if you missed the toast (or have things configured to silently show in the action center without a toast or vibrate as I do) then the visual indicator becomes useless unless you always deal with all notifications the moment they appear. That's.... Just bad design. Don't advocate for it.
Also note that the icon appearing is *the only* visual indicator you get when the phone is set to silent mode. If the icon is already there and you're not looking at the start screen (browsing the internet, playing a game, etc) you will not be notified of a new text message and you'd have to manually check the action center every minute to see if your friend finally texted you back...
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