I actually would love this feature. One common thing that happens to me is that I usually have my Iphone on my desk, I have to get up and go speak to someone for a few minutes, a message comes in etc... I come back to my desk start working, check my phone, say an hour later and see I missed a TXT from my wife because I was away when the chime went off and I didn't think to check it immediately when I got back to my desk. I little flashing LED would alert me that there was something I missed.
It's the same reason answering machines have a flashing light and the same reason mailboxes used to have little red flags. so people didn't have to keep checking their answering machine just to hear "No New Messages" and so they don't have to keep walking out to the curb just to see that the mail hasn't been delivered yet.