Ideally, Seigensou would have needed 24 episodes. With only half of that, the animation team was forced to remove many of of its exposition (worldbuilding is one of the LN's strengths), or to get creative on the adaptation, such as shuffling the events of Volumes 4 and 5.
Let me just say by saying that the first 3 volumes were the weakest parts in the story. If it looked generic to you, then that was the idea of the first three (prologue/worldbuilding) volumes, before the start of the main story clues you in that it's going to be different.
The trigger for the start of the main story, which starts at the very end of Volume 3/ start of Volume 4 Miharu's proper introduction was moved to the very end of Episode 12.
Without this one detail and its implications, which would have happened during episode 9 if they didn't change it, the whole anime was going to look very generic.
Personally, I think the animation director did the right move here as it's the better cliffhanger. Yes, it makes the first season look even more generic than it was supposed to be, but doing it this way lets the story flow better in the anime and allows them to save time. (Apparently with the author's blessing)
Another is how they explained to the viewers that one of the main differences between Magic and Spirit Arts is the fact that the former has a magic circle when you use one of its spells. In the LN it was explained, in the anime, it was by relying on visuals.
If you were to rewatch the instances where they use Magic and Spirit Arts (Celia's demonstration in episode 3), you can actually see that they paid attention to that particular detail.
Volume 3(Episodes 7-8) also took a hit to free up an episode, which is unfortunate since it's actually pretty good. Though there's a good reason for this as Yagumo only really becomes relevant later on.
The most obvious thing they butchered is the fight scenes. No need to explain this one too much, but I can overlook this since Seigensou (at least the earlier parts) isn't really known for its battle scenes.
Considering they took great care in the narrative despite limitations, I can overlook this flaw. They better have a better animation budget in Season 2 though.
Speaking of narrative, apparently there were visual cues that only make sense if you read the latest volumes. I can't speak much about that since I'm only up to where the English translation covers, but that meant that the animation team was familiar with the base material.
In all honesty, it did pretty well for a low budget adaptation, 12 episode adaptation of a series that would have needed more episodes to properly convey the story's exposition.
The animation team (the director especially) knows what they were doing when they made the changes to better fit the medium. And as a fan of this series, I appreciate the work they put into this adaptation.