The flag keeps showing up in Cardinals redesigns because it's the only unique design element they've ever had. Even the piping they use now isn't all that special.
Take the flag out of the equation, and you're left with uniforms any team could wear. Their uniform history is extremely uninteresting, and it's not even consistent enough to be iconic like the Raiders, Colts, or Packers' uniforms are. Recoloring the Jags' uniforms in red and white produces a pleasing result, but it also shows how much Jacksonville's unique color scheme covered for their plainness. Unless the Cardinals feel like radically reinventing their brand, leaning on the flag imagery is probably the best way forward.