I think everyone having mini Ifrits would kinda ruin the primals image since they are viewed as Gods and such to the beast tribes, what i think would be a nice idea would be ifrit recognizing ur strenght trought battle and lending you the power to summon some sort of fire minion or something "Ifrit's familiar" of sorts, they should make it a little diferent from ifrit's own image, just an idea ^_^
What was happening in FF11 with summons was that there were the Avatar Primes, like Ifrit Prime, or Leviathan Prime and Shiva Prime and once youve beaten them, they granted you the power to summon "images" of them with less strength etc etc.