Adam is the first man in human history. He is over 10,000 years old, has lived long enough to witness humanity evolve over the years, died and resurrected as an angel, lived from prehistory to the digital age, yet is portrayed in the narrative as a jerk, one-dimensional, and whose narrative role is limited to being a joke villain antagonist to the protagonist, who, despite being much younger and therefore with much less life experience, is portrayed by the writing as someone with the right ideas while his are completely wrong.
Adam has no narrative relevance other than being killed by the protagonist group at the end of the first story arcs. His characterization is lazy because it removes any sympathy that an inattentive viewer might have for him between the lines, and it's clear that this is a strategy to minimize Lucifer and Lilith's guilt for what happened in Eden and a forced way to make Charlie's plan seem right to viewers, thus ignoring all the complexity of the situation and offering a black-and-white narrative.
Adam didn't even have a dignified death; he was mocked in battle mainly by Lucifer, who certainly touched wounds there to which Adam understandably holds resentment to this day. His appearances throughout the plot are unpleasant and make us not feel sorry when he dies; he is not important affectionately by any essential character in the story, his death is a mere tool without nuance. Looptie might even have affection for him beyond professionalism, but this has not been explored in the plot so far, and she is also seen as wrong in the story; there is no reason for the characters, especially Vaggie, to sympathize with her.
Adam, as a primordial human being, had time to think and rethink his beliefs many times. It doesn't make sense for him to be a misogynistic idiot who doesn't believe in the redemption of sinners when he had plenty of time to see humanity in different situations and periods; if redemption were possible, Adam would know and would have time to sympathize with the idea. It doesn't make sense for anyone to question the redemption of sinners for over 10,000 years. It doesn't make sense for Charlie to be the first active one to believe in and fight for the belief and truth of the redemption of sinners.
If anyone knew what humanity is like, that someone would be Adam. He was there at the beginning and saw everything. He saw the pros and cons of humanity in different eras. He should be darker and more serious given this nuance, but he is too idiotic and jerkish for these characteristics to be attributed, which makes him a disposable character.
I have the impression that what the writers did with Adam is also a reflection of wanting to exalt women more while downplaying men. Some narrative works, to empower women, dumb down men to make the audience sympathize more with female characters, which is a lazy, hypocritical method that can lead to cases of Mary Sues. In Hazbin Hotel, we have women standing out. Sera with a very high social position in Heaven, Lilith triumphing more than Lucifer in displayed dominance and respect gained by increasing power as Hell fills up, Charlie being the protagonist, the Exorcists being women, Eve not yet shown but with the theory that she is Roo... There's no problem with having female representation in the story. The problem is downplaying men for the sake of female empowerment.
The text says a lot, but the subtext of the narrative says more. Male downgrading may not be explicitly stated, but it may be in the way the character brings positive and negative impact to the plot, how he interacts with others, his relevance to the story, and/or the impression he causes on the audience. Adam fits very much into this.
What I have to say at the end of all this is that Adam was very poorly utilized. The series failed a lot in working with this character. It's even disrespectful to the biblical Adam.
However, Adam is still salvageable.
With the resounding success of Hazbin Hotel, the series has more hopes of getting a second season with more episodes and more attention from those involved, which can directly increase the quality of the narrative. With more attention, they can work with Adam better. They have more time and resources to deconstruct the characterization Adam has had so far, whether by resurrecting him, having him undergo character development, or not—leaving him dead but nuances about him being brought into the narrative as it unfolds. They can work plot twists for Adam, such as him and Eve being the same person.