Rather than starting by talking about issues, I think it'll be more productive to look at things in the context of the four types of stories they suggest:
- A What-If style story that explores how Weiss's presence could change the world and canon plot of MHA.
- An adventurous story about Weiss's quest to return home or, failing that, her struggles to build a place for herself in a strange new world.
- A fluffy slice-of-life where we enjoy the small triumphs and trials of Weiss's new daily life in a world where she's surrounded by genuinely good people and humanity isn't confined to fortress cities besieged by a sea of monsters.
- A deeper story focused on the psychology of a girl who finds herself alone in a strange land, after suffering repeated trauma, the opportunity for healing that allows, and the effort required to heal or the effects of failing to heal.
You could easily write a story that only does one of those things. —For example, a story that focuses on Weiss's quest might relegate the canon plot to the background, despite happening alongside it, so a lack of any meaningful changes wouldn't matter, because the focus isn't on those events, and a slice-of-life story might cut out most of the fighting all together, because it's less important than day-to-day interactions between characters.— Similarly, you can write a compelling story that mixes the four of them in almost any combination. Where you run into trouble is when the story awkwardly flirts with all four, while not consistently executing on any of them or presenting a new basis for engagement, and that's the scenario I think Hero or Huntress increasingly finds itself in.
Let's go through them one at a time.
The What-If style is probably the most obvious with this story's setup: If Weiss were to show up on MHA Earth, what would happen? Unfortunately, while Weiss has shown up, we're not seeing that second part. There's been some cross talk between the story of MHA and the story of Weiss on Earth, but it's mostly been on the level of flavor details. People talk about her music and she's the class rep, instead of Ida —not that it's stopped him from filling his canon role, up to and including announcing the alarms were caused by reporters after launching himself into the cafeteria's exit sign in 6-4— but canon's story doesn't hinge on details like who's the class rep and what music does everyone listen to. Similarly, the context for some events in Weiss's story might come from canon, but it's not providing anything unique, to the point where I'd wager you could swap MHA for Sailor Moon and still have most things play out the same way, just by swapping some minor details.
To an extent, this can be excused, especially early in the story. Nothing about Weiss's initial appearance on earth would necessarily change the events of early canon —though there's also nothing preventing her from causing more immediate ripples— and there's actually quite a good argument for keeping things mostly on the rails until class 1-A is established, since that gives you time to establish Weiss's place in the world and a good foundation for the rest of the story. I think the USJ arc is where the lack of change really starts becoming noticeable, because that's the first part where the story has set up the potential for major changes without following through.
While it's from a semi-canon side story, on SB, the idea of Weiss training Yu opens up the possibility of her pre-USJ fight going differently and either removing the need for All Might's intervention or changing his arrival time, in some way. It did neither. More importantly, despite Weiss cutting through her group fairly quickly and arriving in time to aid Aizawa, reducing the pressure from the lesser villains and cutting off Shigaraki and Kurogiri's ability to interfere, things end roughly the same way. Even Weiss's ability to hold off the Nomu and aid All Might didn't really have an impact. Aizawa still takes roughly the same injuries, including the damage to his eye, and needs to be carried out by Deku and Asui; All Might still ends the fight by going past 100% and blowing the Nomu away; and the main villains still get away. Sure, Shigaraki lost the tip of one finger and has an extra reason to hate Weiss, but it's hard to believe All for One and/or the doctor won't be able to fix his finger almost immediately and the extra hatred is, at best, set up for another future change, not a meaningful change on its own.
This wouldn't be a problem if Weiss was proactively doing her own thing, but she's been largely passive, without any major goals, for most of this story. Technically, she set herself the goal of becoming a successful singer, and did just that, but this isn't a story about Weiss's burgeoning music career or the burdens of being an Idol in Japan. She was immediately successful in her efforts, with almost every character we've seen having heard of her and enjoying her music, and she dismisses overly pushy fans with the same easy disdain she does almost every other social encounter. Beyond that, she's already given up on trying to go home, never showed any interest in trying to figure out how she got here, and hasn't even considered looking for anyone else from Remnant. She occasionally chafes at being treated like a 15 year old, despite being somewhere between a college freshman and graduate, but she never does anything about it and mostly goes along with that treatment. She's constantly complaining about the quality of the people around her, or at least her perception of it, but never does anything to change that situation or seek out people she can trust and rely on, despite having much more control over that part of her life than she did back on Remnant.
This is Weiss's story, but it seems like she's along for the ride as much as we are.
The girl who ran away from home and smuggled herself out of Atlas, while it was under military lockdown, has shown no interest in controlling her own life.
It's a bit trickier to talk about the slice-of-life aspect, but the issue here mostly boils down to us just not seeing much of cast's daily life, outside the classroom and the events of MHA canon. Just as importantly, Weiss's internal monologue is dominated by a continuous refrain of contempt for almost everyone around her, it even breaks into moments that are supposed to showcase her trauma.
Which leads us into the psychological aspect. For the most part, I'd say the primary problem has been a lack of consistency, both in terms of how things are portrayed and how they line up with what we know about Weiss and Remnant. I think the most jarring example of this was Weiss breaking down and needing to rationalize the villains as dying from their wounds, rather than as a result of her actions, despite previously not having trouble thinking about their deaths or acknowledging that she had likely caused the indirect deaths of numerous members of the White Fang during the train ride from Mountain Glenn and the Fall of Beacon. Those scenes felt like they would have been more appropriate coming from Bakugo, Deku, or Todoroki after finding out a villain they thought they had only disabled had actually died from their injuries —which isn't hard to imagine, given the kind of firepower they throw around— not someone from Remnant, who was training to be a huntress, and who had already been through everything Weiss has.
On that same note, the idea that the only tool she has for dealing with emotional trauma is halfhearted repression doesn't really make sense. As others have noted, Remnant is big on self-expression and Weiss is no exception to that, with both her music and interactions with others showing off her willingness to express her honest opinion unless something is actively stopping her, and sometimes even that isn't enough. More importantly, grimm are attracted to negative emotions, not the outward display of negative emotions. Just putting on a mask and bottling everything up is very likely to make things worse, so I'd expect it to be actively discouraged on Remnant, even in Atlas. Remember, Mantle's policies weren't just about keeping your emotions to yourself. Their bans were meant to eliminate things that would engender strong emotions in the first place, so there'd be nothing to repress.
Beyond the inconsistencies, there has also been a certain ham-handedness to how these topics have been addressed, which is a major problem for a story that wants to put a strong focus on the experience of psychological trauma and the process of recovery. The hallucinations have been intrusive and inorganic, to the point where I have previously wondered if they were meant to represent PTSD or some sort of external interference and judged the later more likely, despite more recent scenes suggesting that they were supposed to be the former. If the portrayal of trauma makes it unclear that it's supposed to actually be trauma, it becomes hard to have a discussion about its effects or treatment.
At the same time, the treatment portion has been mostly non-existent and now that it's been brought up explicitly, I'm even more concerned. In a story that didn't want to focus on mental trauma, the last chapter might have been fine; just a one-off meeting with an awful school councilor that gets played for laughs and then blown off with gusto. Unfortunately, this story wants to take psychological trauma seriously, which means we need to take its treatment seriously, and that means we were just treated to a scene where Weiss was coerced into seeing a mental health professional who showed no respect for her as a person, any trauma she may have been sent there to discuss, and the very real signs of distress she displayed on entering. Regardless of how it gets followed up, that scene was wildly uncomfortable and kind-of gross.