Is this...I am musing after reading KM's latest article...perhaps the dawn of a new "Monster Manual", I wonder?
With a nice thorough explanation of the term "monster" in D&D. It is more than the creatures that go bump in the night [or try to burn you to a crisp]...but the creatures [emphasis on creatures] that provide threats to PCs in all manner of different ways. To whit...
The bulk, obviously, goes to the "Magical Creatures"[or "Fantastic beasts" or whatever you'd want to term it] section of the book. Your goblins and dragons, demons and giants, minotaurs and centaurs, maybe even your elves and humans*. The "monster" monsters.
Then an "Arboretum" section. For your carnivorous plants, your treants and shambling mounds, myconids, molds and fungi. The "plant" monsters.
A "Bestiary" section. For stats on all of your "normal/real world" animals and their giant/dire varieties. Not just stats for things like lions and bears and giant snakes that you might fight...but things you can use: animal companions, normal mounts [as opposed to pegusi or griffons that would be in the Bestiary], small furry, feathered or scaled critters for familiars. Your "animal" monsters.
Then you have your "Living Hazards" section of the book. For whatever doesn't fit in other categories. Your "trap" monsters.
* Alternately, your could have a "Humanoids" section for PC and "monster" races with extended societal information and sub-types. Humans, elves, dwarves, goblins, lizardmen...your "people" monsters.
I do heartily agree that "trap-monsters" would have "trap monster" stats/info. "monster monsters" would have what we think of as "full" stat blocks AND thorough descriptions. Something that is a "hazard" but not a "trap", might have another "in between" kinda stat block and info.
This is preferable to maintain the traditional MM alphabetical format throughout, and then just say under the name of the critter "trap monster" or "magical beast" or "demonic humanoid" or whatever with the appropriate stat/info.
But I'm not hating the idea of a D&D MM broken into thematic "type" sections (alphabetical within sections, obviously) vs. a straight encyclopedic book.