The system for selecting Pro Heroes in My Hero Academia is incredibly flawed. Heroes are not chosen based on their strong morals or their desire to help people. Instead, they're chosen based on who can get the job done best; who can beat the villains and rescue civilians while looking good in the public eye. Hiring candidates based on skill rather than considering personality may work in other fields, but Heroes should be held to a higher standard.
Heroes are supposed to be the role models of society, yet there are many Heroes and aspiring Heroes who get the job that probably shouldn't. This could be for many reasons. Maybe instead of wanting to protect the peace, they do their job for fame or fortune. Maybe they have an uninspiring personality and would be a bad influence. Maybe they care more about beating villains to a bloody pulp than they do about actually saving anyone. These are the kinds of Heroes who might have the capability to do what needs to be done, but not the personality.
Bakugō, despite his undeniable power and ability, is one of the worst candidates to become a Professional Hero. In the very first episode, he said outright that his goal was to acquire more fame and money than All Might. He not only has the wrong mindset for becoming a Hero, but his explosive personality makes him a bad role model. This inability to give proper responses during interviews was so bad that his entire class had to take a special session on how to handle the media.
It's also horrible what utter contempt he holds his enemies in. That's to say nothing about how he'd told his own "friend" that he should kill himself. At the same time, the way he talks to the civilians he's supposed to be saving is also too abrasive. He acts rudely towards absolutely everyone.
Mineta has plenty of flaws that would make him unfit to be a Hero, but there's one in particular that stands out. It's not that his Quirk is better-suited for support than combat. It's not even his cowardice. It's that he's a shameless lech.
Mineta's perviness makes his morality highly questionable. He's the kind of person who will use the confusion of an intense battle to cop a feel and openly brag about it. It also affects his decision-making; he ends up interning with Mt. Lady, another heavily-flawed Pro Hero, just to end up doing housework for her. This apparent desire for women over justice makes some wonder if he's even serious about becoming a Pro Hero. He seems averse to this idea, but he also doesn't do much to prove it wrong.
Endeavor is a decent Hero but has a long history of contemptible means of administering Justice. Like Bakugō, he holds villains in contempt and only concerns himself with taking them down. He doesn't concern himself with how they got to where they are or if he can help them out on a personal level, a flaw reflected throughout modern Hero society. What's worse is when he carries this type of contempt over to his fans. Some of them are into his attitude like the "Can't Ya See" Kid, but he could definitely stand to be a little nicer in general.
This is to say nothing about his family life. He married to acquire a certain quirk for his children and put his most genetically favorable child through harsh training. However the public feels about him, his family reviles him for his years of contempt and neglect. In fairness, he's at least working on changing this.
Uwabami represents another inherent flaw of a Hero-based society. Many Pros are more concerned with maintaining their image than they are with being actual Heroes. There's a reason Kendō and Yaoyorozu felt uncomfortable when interning with her. They spent most of their time starring in hair care commercials and watching Uwabumi stop for the paparazzi on her "patrol." They had to convince themselves that all this media attention was an important and essential part of becoming a Hero, which it isn't. Having a good public image might be good for being somebody's inspiration, but the priority should be public safety. Uwabumi's Quirk Serpentress is actually really useful for locating villains and disaster victims, so it's a shame to see it go to waste like this.
Eraserhead doesn't seem like he'd be anyone's role model, but he has a reason for this. He rightfully believes that media attention is overrated and focuses on doing his job efficiently, which he's really good at. However, this inattention to his image leads to an apathetic personality that makes him an abysmal role model.
Since Eraserhead normally stays out of the spotlight, his attitude shouldn't matter, but there's still a problem. He works as a teacher at UA, which means that he's directly responsible for molding the minds of budding Heroes. If he acts apathetic and irritable around his students, which he often does, there's a chance that it could carry over into their professional work. No matter how well he understands the Hero business or how well he teaches it, he'll never be able to make his students into the role models for society that they need to be.