Many anime works are based on manga, light novels, or some other form of source material. For example, Sword Art Online, Violet Evergarden, and Mushoku Tensei are based on a light novel. The Quintessential Quintuplets, The Promised Neverland, Horimiya, and Demon Slayer are based on manga. Being published before the anime adaptation, these source materials usually have their own fan base. Any deviation from the source materials will be noticed by those who have read the source materials before.
Producers of anime adaptations are thus faced with the options of staying true to the source material, or developing anime-original content. In this post, I shall explore four examples. A disclaimer: I have only read the source materials for three of them (Violet Evergarden, The Quintessential Quintuplets, and Horimiya) so my comments on The Promised Neverland are more based on online reviews by those how have read the source material and watched the anime.
Let me start with Horimiya. Horimiya is a manga that is based on a web comic called Hori-san and Miyamura-kun. As of now, the manga series just ended, with 15 volumes already published and the 16th (and final) volume should be out sometime soon. The anime adaptation runs a single season with 13 episodes, which is really short for a 16-volume manga. Usually, a single season can adapt about four volumes, so you can imagine the amount of stuff that was cut to squeeze everything within 13 episodes.
But Horimiya is a slice-of-life manga with a strong romance theme. It is really a collection of small episodes, which actually makes it easy for the anime producers to choose which episodes they want to make into anime. The manga actually covers stories about more characters, but by focusing on a handful of core characters and their stories, the anime was able to string together a series of stories that flowed chronologically without having to do much, if any, anime-original changes.
In contrast, Violet Evergarden is a light novel, and when it was being adapted into anime, there were only two volumes and the source material just did not have enough content for a 13-episode season. The light novel also started with the characters already established, and readers slowly discover the background as they read the book. This can make it difficult for anime viewers to understand. This was one of the reasons for making anime-original content for this series. The anime brought one of the background stories to the start, threw in a couple of anime-original characters to help build the background, but otherwise stayed true to those stories which it adapted (except for the ending).
The ending was probably rewritten because they wanted to make a sequel movie for the reunion between Violet and Gilbert. So we ended up with an anime-original twist to the "train hijack" story which was the reunion (and final story of the original two-volume light novel), turning it into an "open" ending allowing for a sequel. The final reunion in the sequel movie actually reused a lot of the light novel's dialogue, just in a different setting. Fans of the light novel (including the anime director himself) would say that the light novel was great as it is. But I think that the anime-original content and changes help to make the anime as strong a story as the light novel. Each is great in its own way, and the anime ultimately remained true to the core themes, concepts, and style of the source material.
The Quintessential Quintuplets started out as a faithful adaptation of the manga series during its first season, but the second season was a lot more ambitious. The first season covered four volumes; the second season covered six. Many scenes were actually cut in the second season in order to bring the season's conclusion at the end of the school trip. And we know that the sequel (either a third season or a movie) will adapt the final four volumes to conclude the entire series.
Like Horimiya, this series has no lack of source material. But what it has is time. With two seasons plus a final season/movie, it can adapt a lot more material. But unlike Horimiya, the stories in The Quintessential Quintuplets are not standalone episodes but more intertwined with each other. Yes, there are occasionally some short side-episodes with no real impact on the story's final outcome. But most of the manga is about the core story. So the second season became quite a hectic rush as it tried to adapt too much of the story in a short period of time, removing every side-episode not fully related to the core story, and even some of those episodes that are. But the anime series has not ended yet, so those related episodes that were cut may still end up being adapted in the final season/movie as a flashback.
As for The Promised Neverland, the reaction of people who have read the manga says it all. The manga has quite a few story arcs, and with the first arc taken an entire season to adapt, this manga series can be a long-running anime adaptation. Except that the people in higher management probably thought otherwise, and the anime was made to end with the second season. Entire arcs were skipped, or compressed in what can best be described as a series of PowerPoint slides. I don't think we can even use the concept of anime-original here.
Back to the topic of this post, which is about anime-original versus staying true to the source. I think the real question is, does it make the anime story as good or better than the source? If so, I don't really see any issue with make changes to the source as part of the anime adaptation process.
In fact, anime, like light novels and manga, is a medium. What works for one medium may not work for another. Anime and manga are close enough that it is easy to have a faithful anime adaptation of a manga. But even then, manga allows the same episode to be told from the perspectives of several characters. For example, the final exam episode of The Quintessential Quintuplets could be told from each quintuplet's view. But this can be confusing and even onerous in anime, which is why a chronological telling of that same episode combining all five quintuplets' perspectives worked better for anime.
Light novels are less straightforward for anime adaptations, since they have less visual source materials to start with. Not having a visual element can limit the expressiveness of a story, but it can also free up that limitations since the author can play on the readers' imagination. A lot more work needs to be done for anime adaptation since anime is a visual media, while novels are word-based. Part of this work may entail making anime-original changes or additions to better adapt the source into a visual form. Like those for Violet Evergarden.
So when I see anime-original changes/additions in an anime adaptation of a light novel, I tend to be more forgiving and accepting as long as it makes the anime a better story. As for anime adaptations of manga, I think the question I still ask is, does it make the anime a better story? If so, I think we can always view it as an alternative route.
Bottom line: if it makes the anime adaptation a better story (compared to not making the changes/additions, and not compared to the source material), I think we should accept those changes/additions since anime is a different medium.