There have been some interesting people who have performed the national anthem prior to the Super Bowl beginning. Cheryl Ladd, for instance, sang the song prior to Super Bowl XIV in 1980. She must not have been awful as no one remembers her performance now, but who knew she could sing prior to that?
The only real criteria for performing the anthem is that one must be American, it seems. No non-American has sang the national anthem pregame of the Super Bowl. This makes sense since the national anthem is about the United States, but only having Americans leaves out a lot of great singers.
While there were a few outliers, the current format of a relatively popular singer doing the national anthem prior to the big game began in 1989 with Billy Joel. There has only been one year since then, Super Bowl XXXIX in 2005, where a choir sang. Otherwise, pop star after pop star has been the pre-game entertainment (Joel has performed the national anthem twice and is tied among singers with Aaron Neville for the most ever).
Of course, we cannot leave out the people who do American Sign Language during the anthem as well. Marlee Matlin has done this three times, the most times performing during pregame of any artist. ASL has been a staple of the anthem since 1992.
Three singers who absolutely must do the National Anthem prior to the Super Bowl
Alison Krauss
Krauss has one of the purest voices in the history of humanity. She can sing beautifully whether she is near a whisper or closer to belting. But she never belts as her voice is amazing enough where she does not need to. The 27-time Grammy Award winner can sing anything from bluegrass to rock, but no matter what she is doing the sound is otherworldly.
Brittany Howard
The Alabama Shakes vocalist can do whatever she pleases with her sound. She can emote, rage, and offer the most interesting sounds about the tenderest of feelings. Brittany Howard's voice is undeniably incredible. She would give the anthem a full sound filled with passion.
David Byrne
Byrne has a unique quality to his voice. He does a lot of things with his instrument theatrically, but he can also just croon a tune when he wants to. He has always been an underrated vocalist. Plus, the world just needs more Talking Heads in it.
Glenn Danzig
Maybe an odd choice, but Danzig can really sing. He has good range with a clear voice and there would be no issues with his volume. Plus, seeing Danzig do the national anthem would just be cool.