Ward turning out to be a HYDRA agent may have been Daisy's biggest regret, which would explain his presence in the framework.
For a while, that was my thought too, but it didn't make much sense even at the time. Mostly because Ward being HYDRA had nothing to do with Daisy, so it couldn't be her regret, and Daisy hadn't entered the Framework via Aida who was the one running the programs that uncovered ones regret in order for the Framework to address it.
To be honest, I had a lot of issues with the Framework storyline as it was airing, Ward being one of them. I was also put off by the idea of May being wholly HYDRA, and Fitz being evil made no sense to me. Not when you consider how it is the Framework was supposed to work and how the characters were behaving beforehand. There were too many inconsistencies between the rules and the results. Until I figured something out.
Aida is a lying liar who lies.
(This is going to get long, FYI.)
The showrunners claim that through the power of the Darkhold, Aida was able to create a complete replica of Earth and all the people on it. So, they have at their disposal every single character that had been on the show previously. Fine. The alterations between this Earth and the Framework Earth is a result of the regrets the Framework fixes for each of the 7 people Aida put into it: Agnes, Radcliffe, May, Mace, Mack, Coulson, and Fitz. Agnes got her health and a life in paradise on a cute island where she can relax and spend the rest of her the days painting. Radcliffe just wanted to be with Agnes. Done and done. May, the first one in, regretted having to kill the Inhuman girl in Bahrain. As a result of that HYDRA was able to use the girl to stir up anti-Inhuman sentiment. Well, ok, I can see that. But we'll put a pin in that. Coulson had regrets about joining SHIELD and so we see a Phil Coulson living a small life away from the danger and intrigue of being a super spy. Mack clearly regrets losing his daughter. Boom, Hope lives! Mace I guess regretted not being a true hero? Hmm, things are getting a little iffy, using the show's own logic of how the Framework is supposed to work. And then Fitz. All the other characters foreshadowed their Framework selves in dialogue. Coulson was saying to May maybe he should never have joined SHIELD, we all knew May's biggest regret, Mac's regret over Hope was heavily hinted at in previous episodes, and Fitz... well, he was most upset by creating the technology for SHIELD that ended up doing more harm than good. The only time his father was brought up was when Radcliff mentioned him and what an ******* he was, or Fitz stating how glad he was to never speak to that man. Doesn't really seem like a regret to me. Yet Fitz's Framework fix is his father being in his life. So that being his regret is iffy at best, a pure gimmick to make evil-Fitz at worse, or a hint about the true nature of how
Aida runs things in the Framework. I don't think Aida was simply following her programming and was forced to simply react to how things played out. I think she had a direct hand in manipulating that world for her own benefit, including how our heroes behaved.
And I am basing this theory on several things, including what Aida says to Ivanov about May "breaking free from her narrative". And now we're back to that pin in May's regret and the results thereof. While the idea that HYDRA could have used that little girl to create anti-Inhuman sentiment, the idea that May would go along with everything else HYDRA is just because of her guilt is a stretch based on who we all know May is as a person and an agent. So why is she fully Team HYDRA? Because Aida said so. Because Aida needs May on her team.
Once the fact Aida has an ulterior motive for placing them all in Framework was revealed, how they were all behaving in the alternate universe makes a lot more sense. Aida needs a human body so she can have free will. The Darkhold showed her how to do that, but she needs someone to build it for her.
She needs Fitz. The Framework and the events that are unfolding aren't a natural progression of choices May, Coulson, and the others made. Aida has manipulated it all to put Fitz at her side and under her thumb.
May: she regrets shooting that girl. The Framework does erase that. HYDRA uses it to set up a world with more control, which also gives Aida the means to control.
Coulson: he becomes a history teacher instead of a SHIELD agent, via his regret about joining SHIELD. But are we really supposed to believe that just one man not becoming an agent is the thing that allows HYDRA to win a decades-long battle? That NO OTHER agent would be able to stop them? I love Phil, but he's not the only capable agent in SHIELD. It only makes sense if Adia altered Phil to be the kind of guy that follows all the rules because she had to keep him away from the others, knowing his slightly broken brain would break free from her programming the easiest.
Mack: she kept him away from joining the fight by giving him something too precious to put in danger of losing.
Mace: Not sure how anything he regretted would lead to him suddenly being Inhuman. But Aida already knows from her experience with May that humans need a conflict to keep them engaged and she needed something to keep everyone busy so they weren't paying attention to what she was really planning. Boom, Mace is the Inhuman anti-HYDRA rebel leader to give the others an enemy to focus on.
Jemma: in the Earth created in the Framework I'm sure it's possible that a bunch of SHIELD agents got shot. OR Aida got rid of the only person that could tear her and Fitz apart.
Daisy: Aida recognized that Daisy could also have been a threat, so she's kept close but Aida also needs her happy so she gives her Ward, even though we know Daisy loved Lincoln. But Aida can't risk Daisy discovering her true Inhuman nature, so she keeps her close to the one person that would betray who he works for, (Ward), to keep that secret. If Daisy had Lincoln, she might have discovered her powers and thus become a threat.
Fitz: If the show had followed the same path with Fitz as they established with the others, Fitz's regret would be about the technology he created while working for SHIELD. Fixing that regret is the complete opposite of what Aida needed. So she
created a Fitz that she could make work for her, inserting an abusive father and programming a relationship between her and Fitz so he'd be devoted to her without question.
Everything in this alternate Earth has been manipulated and arranged to benefit Aida and her goal of making a machine that could give her a human body.
By having Aida be the one behind not only HYDRA in the Framework but also the one who was able to manipulate everyone the way she did makes her, to me at least, an even more formidable nemesis. She not only found a way around her own programming, but she had a long-term, multi-faceted plan, that she nearly executed perfectly. The true fault in her plan was her own reactions once she could experience human emotions.
TL;DR: Fitz would never actually be that evil. Nor would Phil be that cowardly. And Ward was only resurrected to keep an eye on Daisy (who was still Skye).
The funny thing is, in some ways the Framework did all of them a favor, (except Fitz for a while there... or Jemma), because it showed May a possible outcome if she hadn't shot that little girl, Phil a vision of his life had he not joined SHIELD, Mack got to spend more time with his daughter, Daisy even got to have some closure over Ward and maybe see him as he could have been had he been given a chance to rise above an abusive past rather than preyed upon because of it. Fitz now has upgraded a level in badass, but at a pretty big cost to his own piece of mind. I guess maybe Jemma got to prove to herself that she'd also cross universes for Fitz as he did for her previously but is that something one needs proving in order to accept they belong with someone? And she already leveled up in badass in S3.

It did prepare her a little to deal with Kassius the Fascist Smurf, I guess.