They could do that, and it would make a good story easily and make sense. But it would be like taking the death of Peter Parker's parents and giving that story to Daredevil. Or saying the Hulk is an alien from another planet sent to Earth by his alien father before the planet was destroyed. Since this is fiction you can do that, but this has always been one of Hank Pym's MAJOR and maybe only vital stories. Hank has always been the creator of Ultron. His character has always been this self loathing guy who creates the greatest AI but it backfires and becomes his greatest failure. Its part of Pym's character. Whereas Tony Stark, while it would fit in and be a continuation of what we have already seen, isn't a failure in the same way. Stark is in fact one of the examples Pym uses to tell himself he is a failure. Stark is a former friend, he is rich, famous, smarter than Pym, and always succeeds in everything.
This is how I see Ultron's psychology in the comics, he was created by Hank Pym. Pym has always suffered from several severe mental problems and illnesses, anxiety, self doubt, self loathing, depression, schizophrenia, resentment of those around him, and on and on. But he takes medication, and he doesn't really hate the Avengers/ his friends and his wife and himself, but a small part of him does.
He used his own brain patterns to create Ultron's mind.
When Ultron became evil and started killing and attacking humanity and especially the Avengers and Pym and Janet, it was almost like Pym's dark side attacking everyone.
To me, Ultron represents the dark side of Pym. The one he tries to hide, ignore, and take medication to try and make go away. In my opinion Ultron's psychology has always been that he was given all of Pym's fears, doubts, hatreds, loathings, resentments, angers, anxieties, etc. He hates the humanity, the Avengers, Janet, and especially hank Pym, because deep down hank Pym does, even if its just the smallest amount.
Also, He used Janet's mind to create
Alkhema, a mate for himself.
To me its like Hank took all his dark feelings and thoughts and made them real and alive by putting them in a robot body. Almost like on Dragon Ball where that one guy tried to banish evil from himself and created an evil clone version (Piccolo?).
So, to me, Ultron is also like the son who is taught by his father (Pym) to hate and be a bigot. He is taught what to hate and fear. Then Ultron goes on to have his own son (Vision) and tries to teach him what to hate and fear. But now the reformed grandfather (Pym) steps in to save his grandson (Vision) from that same life of bigotry. And Vision joins the Avengers.
In other words, Ultron hates humanity, and the Avengers, and the Wasp, and especially hank Pym, because his mind is a copy of Hank Pym's mind, and his robot programing cannot read it correctly. Or like the AI character from Green Lantern, he can only focus on the darkness because thats all his mind was given by Pym, and wants to destroy humanity because his robot feelings cannot process the pain.