While it's noble to pick such things like some kind of totem animal, a team wishing to emulate the swiftness of Eagles or the strength of Bears, it does seem a little outdated. Modern audiences are different creatures altogether.
Oakland has the right idea, I think. They've got the Raiders, which essentially are pirates. What we really need, whether it be teams like the Ravens or Texans who move or new expansion teams like Carolina or Jacksonville, is more modern mascots to represent these teams. I know I for one would be a lot more interested in watching a matchup between the aforementioned pirates and, say, the Nashville Ninjas. A Cardinal is hardly a fearsome symbol, so that franchise could become the Arizona Zombies. We actually already have Cowboys, so that's a huge plus. Detroit should drop the Lions...well, the entire team really because they suck. But assuming that team still counts for anything rebranding them the Detroit Robocops would certainly get people interested in them for a change.
I don't know. I can't help but think this would be a phenomenal idea. So long as nobody goes overboard with it; I could see the someone like the Pats taking the new name of the Chuck Norrises, which would hardly be fair to the rest of the teams. (Though I suppose it would explain why those guys always win...)