And to top all that, they were thrown in a school setting, which is the laziest idea to use, but also the most successful one because everybody can relate to something they were part of for at least a dozen years of their lives.

The school setting is necessary specifically because of the source of Haruhi's melancholy. Specifically mentioning that the things she experiences at school are that which everyone does, the monotony of the setting, how unteresting and normal it is, is integral to Haruhi's dissatisfaction. And the series does not focus that much on school anyway, as Haruhi desires to escape that monotony, leading to the other settings throughout the show. The series has its place being at school, as most other settings wouldn't emphasize the normalcy as much, so this isn't really laziness under the backdrop of Haruhi's character arc.

I too liked them as ideas but I was never made to love the show because of them, since they were nothing more than gimmicks.

Sure it is a gimmick, but there's a bit more to it narratively. The aliens, time travellers, and espers and how they perceive Haruhi as an entity, is relevant in that what Haruhi needed was to be acnkowledged as simply herself rather than a supernatural entity, which Kyon in contrast to the rest provides. By featuring these supernatural characters, it emphasizes Kyon's place as effectively the one person human to Haruhi, her one tie to humanity against her desires to escape reality. Their existence and Haruhi's inability to know about them reinforce the fact that although she wants this supernatural world, what she needs isn't that at all. By the end of the series, the emphasis is moreso on finding value in the mundane than through these aliens, time travellers, and espers Haruhi persues.

Unfortunately this illusion breaks very easily, once you realize that in her quest to have fun, Haruhi is manipulating people for her amusement. As much as they try to tell us the world is her creation, and she can do anything she likes with it, it eventually comes down to treating people as nothing but toys. This essentially makes her a bitch who cares only about herself. She is like a spoiled kid who thinks it is the center of the universe and everything happens for its amusement.

The setup of the series certainly involves that, but it's clear that the conclusion the series is in direct opposition to that. Haruhi's return to the normal world after her attempts to escape to her constructed world signify her rejection of escapism, and in effect rejecting her role as god to become more human. There are several instances chronologically after that point which showcase Haruhi has grown past simply doing whatever she desires. The baseball episodes has her coming to understand Kyon's desire to stop playing, which prompts her to give up, which only works as a logical conclusion to her character arc in the melancholy episodes. The island episodes showcase moments of Haruhi genuinely caring for others, for the murder, the wellbeing of Kyon's sister because of the murder, and of course Kyon during his moment of unconsciousness. The computer club episode even has Haruhi willing to sacrifice herself for the game, rather than Mikuru and Nagato, by Kyon's suggestion, a pretty clear signification that she gives into influences at this point and despite her pride is able to put herself on the line. And of course, the concert episode showcases her empathy for the band members, knowing that she would have had their motivation to keep playing if she were in that situation. The rain episode does a good job at highlighting the mundanity aspect of the series, emphasizing that all the absurdity present isn't necessary for Haruhi. She doesn't need to be god and escape reality; she can embrace the little moments.

The show does its best to distract the audience from realizing what a bitch Haruhi really is, by having a non-linear plot in the first season. The events were told in a scrambled manner, thus making it feel like the whole thing was a mystery that needed to be solved by the viewer. Everybody was so obsessed with finding hints or how everything was foreshadowed ten episodes ago, to the point they completely overlooked the simple fact that they were cheering for an awful person who was playing with peoples’ very existence for her amusement. This was one of the biggest revelations the second season offered when it told the same events in chronological order. Since by then the mystery was solved, rewatching the events in a linear fashion just couldn’t hide the truth anymore.

If anything, the non-linear order would make it easier to have those problems with Haruhi, as her moments of growth are all over the place, while in the chronological version it's far clearer to see the implications of how she had changed throughout the episodes.

He even gets to solve the conflict of the whole series by essentially kissing Haruhi, further making it feel like she is a typical date sim girl who needs a man to fix her psychological issues with his D.

The kiss works well because it emphasizes the necessity of human connection. Haruhi likes Kyon because he was the one person to appreciate her as who she really was. The one person to perceive her as a person rather than a supernatural entity (like the rest of the brigade) or someone crazy (like everyone else). Of course, romantic impulse has to do with it, and Haruhi's claiming of love being a disease yet acknowledging that she cannot escape desires such as love emphasizes that this is an aspect of humanity that her eccentricities cannot escape. Kyon is the only one to be brought to her new world, because despite her attempts to cut all ties and escape to a more interesting world, she couldn't cut her main tie to humanity. It was that kiss which emphasized the human connection Haruhi actually needed, rather than everything she was pursuing. Her interactions with Kyon after that moment became more integral, and she was more prone to giving up aspects of her selfishness. What she needed was to forge meaningful interactions with others, which that conclusion was building upto.

The infamous Endless Eight arc, where it repeats the exact same events for eight episodes in a row, is seen as a very lazy excuse to prolong the series.

The Endless Eight didn't need to be that long, but it's not quite just a lazy excuse to prolong the series. They made enough out of it through different details each episode and re-doing them to their entirety rather than simply reusing them. It provided more weight to Nagato in Disappearance, and the meta aspect it provided was appropriate for a meta show like Haruhi. It in essence highlighted the tendency of anime watchers to effectively go through the same events week by week. Simply watching anime and repeating the process, in effect doing the same thing with slight variations. Which endless eight represents to the extreme. The fact that Endless Eight aired during the summer further reinforces it, as it draws a parallel to the never-ending summer of the show, especially since such repetitions of useless activities can be common during breaks such as the summer. Of course, 3 episodes would have been overall better, but endless eight worked well enough. Those who chose to pursue it must have been aware of the backlash it would result in, yet they still chose to follow through with it, utilizing it as payoff for Disappearance.

They are defined by a generic school uniform, and some minor accessory like yellow ribbons in their hair.

The majority of Haruhi's main cast is indeed lacking, but Haruhi herself has much more than merely her yellow ribbon. Her sense of melancholy was well contextualized, her eccentricities added interest to her character, and some growth was there. Her acknowledging of her human impulses that she ideologically opposed but physically could not overcome, her belief that the world is indeed grounded despite her desires for something more supernatural, her struggle to come to terms with appreciation, and her eventual overcoming of her melancholy through merely acting and finding meaning through whatever action she pursues were nice character aspects.

Overall, your review greatly undersells the series. Of course it has moments of pandering that only hinder what it's going for, but it overall does a good job with its arc, and captures the sense of melancholy well, through additional aspects such as how the series tries to establish awareness but hints at so much beyond the characters' awareness that it confounds them, and how the scattered nature of both the show's content and its airing order complement the feeling of being lost and all over the place.

The Haruhi series may have inspired a lot of moe shows that overall negatively impacted anime as we know it, but it's a worthwhile work that has some substance to it.