The traditional trilogy came to be because the rules were more detailed and the line between player and DM was deemed nothing less than sacred. The DMG's biggest section was about treasures. It clocked around 50 pages and had Gygax been able to, he would most probably have included all the monsters in the DMG but it was already twice as large as the PHB. And so, that is why we came to have three core books.
DMG 1st edition preface: As this book is the exclusive precinct of the DM, you must view any non-DM player possessing it as something less than worthy of honorable death. Peeping players there will undoubtebly be, but they are simply lessening their own enjoyment of the game by taking away some of the sense of wonder that otherwise arises from a game which has rules hidden from participants.
Once you decode the hilarious prose from Gygax, you can see the intentions were good even if it's kind of misguided. Had people listened to Gygax and insisted on "DM secrets" being the proving of a select few, the game might not have grown so much. But there is merit in the intent even if Gygax's execution is flawed.
The rules and elements contained in the books are a language. Contrary to what Gygax thinks, everybody should learn it. It's once you apply this language and form sentence with it (creating an adventure, or a campaign world) that you have "secrets" to make your players marvel.
Anyways, here's what I would do:
Core book I: DnD Game
Where you learn all the basic rules of the game, how to create characters, how to create groups, how to play, how to DM. Task resolution, abilities, classes, themes, whatever. Adventure creation tips. Dungeon and town generations. How to customize the game and other core books. Put main spells for a 1st level character but that's it. All kinds of equipment.
Core book II: Tome of magic
Put a crapload of arcane spells and magic items. Also put guideline on customizing spell lists items for specific campaigns AND a system to create new spells and items.
Core book III: insert fancy gygaxian name that means "Divine stuff"
Put divine spells in there but also make this a sort of mini-deities and demigods book, with customizable religious templates. Maybe look at
Book of the Righteous and go from there.
Core Book IV: Monsters and denizens
By all means have all kinds of monster staples but don't stop there. Put a crapload of stat blocks for typical guards, nobles. thugs and other NPCs. And then have interesting system and guidelines to create your own creatures.