the training data is not stored in the model in its original form,
It is not stored in the model, period. Same as you do not store the shape of the letters you’re reading right now, not even the words, but their overall meaning. Remembering the meaning of what I write here, you can then produce words and letters again and you might be close but even with this short paragraph you’ll find it very hard to make an exact replica. That’s because you did not store it in its original form, not even compressed, you re-encoded it using your own understanding of language, of the world, of everything.
Why would you hire a photographer instead of renting a camera, then?
…because you know shit about photography (I presume, for the sake of argument). Why would you hire an AI artist over doing it yourself, then?