I have no idea if the devs are reading the forums and even less if they will notice my humble reply among a myriad of other replies and opinions but well, I think I'll share it here.
I am one of the few who were not disappointed with the story in its current incarnation, as I took it as being a deliberate throwback to Banjo-Kazooie's original, rather simplistic narrative. I was more interested in the characters and the setting it sets up for a potential prequel/sequel ; to me, especially given its ending, it is obvious that what we are getting here is a vertical slice of a greater tale and that, just like Banjo-Tooie radically expanded upon the original's world, the follow-up (or prequel) to Yooka-Laylee is where the REAL story will be shown.
However, if I was asked to do changes? Well...
If the changes were to be just minimal/events-wise, I would start by making the intro a bit more elaborate. Notably, once you get inside Hivory Towers, to have Capital B contact Yooka & Laylee and invite them to his office, where he'd apologize for stealing the One Book then compensate them with money to con them into giving it up. After returning to the lobby, Laylee would hear the Pagie atop the gold statue, leading Yooka to investigate and find it. After learning the One Book's true purpose, the duo decide to stay against Capital B's wishes, beginning the adventure for real.
Likewise, through the game, have the duo more consistent ; focus more on their unique traits (Yooka being yearning for adventure, Laylee using snarking to cover up her feelings, this new duo being closer than the original one relationship-wise) and dropping the Banjo-Kazooie-inspired catchphrases, instead letting the new duo shine on its own.
I would have more cutscenes between worlds, setting up the V.I.L.E story arc better, maybe showing bits of Yooka's and Laylee's background as you progress too, showing how this wasn't their first adventure or how they feel about all the insanity they run into.
For the ending, drop Blasto from the finale and have the finale more somber ; have the duo know that while they thwarted the immediate threat, that they realize that what they witnessed and stopped was just the tip of the iceberg and that ultimately, Capital B, though corrupt, was just one more pawn in a scheme much greater than all of them. Simply put, end on a 'and the adventure continues' note instead of a half-assed party.
If a total overhaul and heavy gameplay changes were possible...
Since this is a writing/book-themed setting, take full advantage of it.
Change the intro, shorten it. Don't show the villain side's intro at first. Just start with the duo chilling on their rock... then suddenly, their book is stolen. But just as they try to set out to get it back, the entire world start having seizures and everything become warped and weird, with strange green voids filled with letters and massive rifts opening everywhere.
When the duo make it into Hivory Towers, the place is an absolute mess ; progressing forward is impossible because reality-altering rifts and gigantic tears in the fabric of space physically stop progress. Meeting with Trowzer and the first Pagie reveal that the book that was stolen was the One Book and that Capital B just wrote something into it. The One Book being the source of reality, his amateur writing attempt had disastrous results, tearing the world apart and scattering the Pagies through its fragments ; for the world to return to normal, the Pagies must be recovered and the One Book, restored.
The duo would then settle to recover their story and regain control of their own lives.
Unlocking and expanding Grand Tomes would also be different thematically. Instead of 'unlocking' and 'expanding', what the duo is actually doing is undoing the damage Capital B did ; every Grand Tome world was torn apart by the same waves from the start of the game and by using Pagies, that damage can be undone and the worlds, repaired.
Likewise, as you get more Pagies and Quills, you progressively repair Hivory Towers as a whole too, progressely putting back together its fragments and removing the large voids everywhere, making the bridge toward Capital B's office.
This would also justify why the Hivory Towers employees are so mixed about the duo ; they're nominally supposed to fight you but most of them were trapped by the world-altering shockwaves and are thankful to the duo for rescuing them (or ask them to do things). Only actual enemies/bosses have an actual beef with the heroes and actively try to kill them.
Events-wise, I would rebalance quests a bit to account for the characters' new traits compared to the old duo. For example, I would have Yooka undergo character development regarding his excessive thirst for adventure, with his blind acceptance of quests without making sure it's a good idea resulting in a disaster in at least one of the worlds. This would alter the world in a radical way (akin to what World 5 did with the Star Wars parody sequence) and open a bunch of extra quests, in which Yooka would need to fix his mess. On subsequent quests of this type, Yooka would learn not to trust characters blindly and come up with Laylee for ways to cheat hostile characters out of their Pagies instead of playing along the next time they run into such situations.
Another example would be Laylee falling into a Kazooie-type sociopathic spree due to stress and frustration... eventually leading to a NPC either snubbing them of their reward, screwing them over, or somehow deciding to lead them into a trap as revenge. Leading Laylee to have to face her insecurities and be more frank (and a bit nicer) in her interactions instead of hiding behind her snark.
In short? Make quests dynamic, changing varying on the order you do them. Use chains of quests to create story arcs, if not accross worlds then within single worlds at least. Use them to flesh out the characters as much as justifying gameplay and jokes.
All of this culminating with having the cliffhanger change varying on completion. If you don't get all the Pagies and restore the One Book, the duo never learn that Capital B was a pawn due to Dr.Quack silencing him (potentially via... an irrversible process) and then leaving, our duo not getting anwsers. However, if the full One Book is restored and the world completely repaired, the duo learn of V.I.L.E and how, despite being corrupt, Capital B was only really interested in profit, not destroying the world and how he had tried to use the One Book to set himself free only to screw up because of his selfish wishes and his unability to handle the Book's powers.
The game would end with the duo sealing the Book for now and preparing for their next adventure, knowing that as the new unnofficial guardians of the world's most dangerous artifact, it is only a matter of time before someone else, in particular V.I.L.E, come after them.
If we want to go a step further, integrate the fourth-wall breaking into the narrative ; as a writing-based world, character roles and narratives are a fact of life for the characters. This can be played for both humor and drama ; having Capital B mocking the duo over how they think he's a villain when he's just trying to make a profit or having the duo complain about how every NPC is shoving their problems into their hands just because they were chosen by the Player.
On the more dramatic side, Yooka feeling insecure from being chosen by the Player and feeling pressured to accept every quest he come accross because he's scared of failing in his designated role.
This could even tie to their background ; Yooka as a novice and rather unimpressive player character type whose desesperation to prove himself and desire to actually do something of his life clashes with his fear of screwing things up and unability to accept that he can't help everyone. On Laylee's side, I'd picture her as a former respawning minor bat enemy who hide her insecurities from bullying due to her large nose + her fear of being expendable behind her snark ; she is afraid that if she doesn't snark and defuse any serious situation, the narrative will end up in her death for the sake of cheap drama due to her life having 'little value'.
Ultimately, the goal would be to integrate the story and gameplay as a whole. To have both complement one another ; the story actively become developed as you play the game with less need for extraneous cutscenes and instead of having to be inserted awkwardly, become a source of new events and gameplay design for the game.
But then, I guess I'm a weird person and I'd guess that such a thing would require far more budget than the game got...
I don't know if anyone else would like that. I do realize that it's probable that I'm 'missing the point' of the setting.
But if you asked me, this is how I would go about it without changing the cast, locations, and gameplay.