There is a 3rd party program called Kate (used to be Caterpillar), which among many other things allowed you to customize the notification settings. I used Caterpillar way back when with a Jailbroken iPhone, so I don't know if they are offering their products through the legit channels now or not (mind you, it never worked consistently).
You can find them here. It looks like they are still offering this product, but may be not through the App store. You would have to install it yourself, so proceed at your own risk:
http://ripdev.com/kate
I too brought up this feature way back when I bought my first iPhone. It is simply absurd. Apple or someone else will hopefully address this ASAP.
+And as for Mr Anderson, this is not something that would be pointed out on the specs of a device. Even the simplest analog answering machine way back in the 1980's had a persistent beep to notify you if there were messages waiting for you. And EVERY cell phone I have EVER owned has had this feature, so it is perfectly understandable that those of us who find this a great omission, would like to voice our discontent.+
+As for this NOT being the proper place to ask for feature requests, you are plain wrong. Many a times there are workarounds and 3rd party solutions that we would never hear about if everyone was to simply submit their requests to Apple. Also this is a great way to find out if others share your point of view or not. Even if Apple does not officially read these forums, I can guarantee you that given enough critical mass behind an issue, they will find out about it. I know, because I happen to be a software developer and have experienced this many times first hand.+
Thank you EVERYONE for sharing and posting even if you are don't have as many posts as others...
Message was edited by: Shahin
Message was edited by: Shahin