"doesn't follow through on the premise very well" seems a common complaint about light novels. I think the format puts a lot of constraints on what you can do, but writers come into the thing with a lot of big ideas. One important thing is that editors are going to want a casual reader to be able to pick up any of the novels in the series and reasonably follow what's going on, in just that one novel. Links to previous novels will be kept to cameo appearances of popular side-characters, and vague references to events only.
You can clearly see the "seams" in some LN adaptations where they fit the novels to the episode structure. For example the anime of A Certain Magical Index and a similar series Strike The Blood both suffer from the same structure. There are 4-episode arcs in both shows which almost all seem to follow the same exact pattern: Episode 1 start with hero's "daily life with main girls". Then, "girl with problem" is introduced who is hunted by "monster of the week". By episode 4 of the arc, "monster of the week" is vanquished and "girl with problem" is saved.
... Then mood whiplash happens because on the next episode, they're back to "daily life with main girls" and all side characters introduced in the previous 4-episode-arc suddenly disappear: this is not a fixable problem - it's a new book now, so the chaff needs to be cleared away in order to clearly tell a new story for that book.
If you liked a new girl from the previous novel you're outta luck, since they're now relegated to an obligatory 2-minute cameo appearance in each new novel: this can get really predictable, since the editors don't want fans of any one side-girl to get upset that their waifu didn't appear in one of the novels, so they end up needing to contrive ways to have all the girls do cameo appearances. If they're dumb writers, they just happen to come across one of the girls at the subway station when they're going somewhere else, and if they're smarter writers they'll fit Previous Girl into the story in a more organic way: maybe she's a hacker so once every novel, they need to hack something or use her computer-fu (which could introduce some weird fridge-logic: before they helped "hacker girl" in one novel they never needed a hacker, but now they seem to always end up needing a hacker in each story). However they fit them it, it's still done because they needed to cram everyone's Best Girls into novels where they don't belong, rather than because the story required it.
These are Dime Novels basically. Each individual novel is going to follow a similar genre-driven format. The same as pulp detective novels all follow similar patterns. Worrying about the "overall plot structure" of most light novels is like complaining that you read all the Phillip Marlowe books by Raymond Chandler and you didn't think much of the overarching plot.