School Status Quo
The series's initial setup of a powerless child who tries to get accepted into a superhero school was a perfect starting point. It made world building focused, gave our protagonist clears motivations, and introduced a large supporting cast. U.A. has now turned into a setting that consistently hurts the momentum of the series. Every time there is an arc that challenges the status quo and moves the narrative in an interesting direction, like the Hideout Raid or Pro Hero Arc, it is then followed up my storylines that take place entirely in an academic setting. While these school arcs are not outright bad they lack a crucial element: tension.
The tension in academic arcs is negligible compared to the ones that proceed them, since the controlled settings of U.A. and its affiliated organizations are free from any real danger. While lower-stake story threads are important the lack of tension is worsened due to the length and odd gravitas given to MHA's take of these plotlines. A perfect example of this is the Joint Training Arc, the most recent example of this, which consisted of 23 chapters, running from chapter 194 to chapter 217. This might not seem like an issue until you consider that it is only 4 chapters shorter than the Forest Training Camp and Hideout Raid Arcs combined. Major character beats such as Tokoyami showcasing a new form and Deku unlocking a power occur in the arc but since they both take place in mock battles that are basically extreme versions of Capture the Flag, they lack the weight and impact that they could have had.
Having villains attack during these academic storylines would be a poor solution since it is a card that the series has already played twice and doing it again would seem trite. A better approach would be to simply shorten the length of the arcs and tie them in more directly with the more impactful plots to follow. Touching upon the academic side of things might be important but it should never bog down the narrative at large.
Bloated Cast
As previously mentioned ,a large assortment of characters has been a part of the series's identity since its inception. The rate new cast members are introduced has not slowed down which has caused many pre-established players to get sidelined as new ones take the lion's share of the attention. This has proven to be detrimental to several major characters like Uraraka and Midoriya who, despite being the protagonist has taken a backseat for months at a time. Even the Joint Training Arc only incorporated him at the start and the end with this momentum for his character being cut off once we get into the Meta Liberation Army Arc.Trimming down the cast and making sure that our main characters have active roles in plotlines is a good way of fixing this problem. Reduction could come in the form of killing off minor and major players, though this seems unlikely since MHA has a tendency to avoid character deaths. Another way of slimming the roster is to give characters a natural and understandable exit from the series, writing them out in a way that still maintains their agency. Fugo leaving the crew in Jojo's Bizarre Adventure is a great example of someone leaving the narrative with a clear motivation: he does not want to oppose the gang so he decides to get out while it's safe.
Limp Villains
Now we come to what may be the biggest recurring issue in the franchise: inconsistent antagonists. The villains of MHA all tend to be underwritten in one way or another. All For One was a puppet master who was built up as the ultimate threat who upon his first true fight in the series---used a dull combination of abilities while wearing an over-designed mask that made it impossible for him to emote. Upon his defeat he is then reduced to cameo appearances. Overhaul's minions declare that their boss treats them like a real family, but we only see him either killing people in cold blond (including one of his own men), trying to murder heroes, or torturing his own daughter! We are told the Overhaul is a gangster with a heart of gold but nothing we are shown ever backs that up.
The worst offender in this regard has to be Shigaraki who is possibly the dullest character in MHA. He can be boiled down to a violent nihilist who just wants to destroy hero society because he sees no point in it, which is a motivation that would be serviceable if Shigaraki felt like he was actively trying to uproot the world. Instead 70% of the time he is just sitting down and grinning. This one-note personality and showing no agency makes him boring and difficult to engage with as a reader/viewer.
While the previous points are relatively simple to fix the villain problem is more complicated. While antagonists such as Stain or Gentle Criminal are highlights in MHA since their simpler motivations gave way to more direct interactions and streamlined conflicts it is hard to see more villains like them appearing in the future. Both were ultimately street-level threats that ,with the series heading towards what seems like an all-out war, its difficult to imagine simpler baddies like them showing up as we build to an ultimate conflict.