Creature type would not have been a good way to organize the 2024 MM.
They altered the creature types of many creatures to better balance out how many creatures belonged to each type. That would have been confusing to so many people who try to look up military hobgoblins in the Humanoid section, among other changes.
The line between creature types are a lot more blurry now. Heck, each Naga is a different creature type. In fact, creature type, planar origin, and habitat are among the most ignored or house-ruled qualities of monster entries. Some say that more monsters count as Fiends. Some say that Goblins are Humanoids.
In a way, organizing by creature type is old school. Since AD&D 1e Monster Manual, the Fiend type (Devil, Demon) was all in one place, under "D". Dragon was all in one place. Elemental was in one place. Later, Beast was often separated out into one place. Sometimes, Humanoid (NPCs, rogues gallery) was too.
Organizing by creature type is a normal way to do D&D. Traditional.
Old school didnt have a Feywild yet. At least core didnt. If it had, the very many species of "wee folk", plus Goblin, Hobgoblin, and others probably would have grouped together under Fey or "Faerie". But early D&D adopted a euhemeristic tone, where all Fey were treated as if Humanoid (literally "demi-human" and "humanoid"). Today, all the Fey in one place is helpful.
A separate section for Humanoids is helpful, and the intro to the Humanoid type will mention what this is. It is defined by its "profession", referring to the ability of the species to learn, teach, and form human-like cultures. In 5e core, the term "soul" is official but remains undefined. The nature of a Humanoid soul is worth mentioning as an aspect of this creature type.
Regarding Goblin and Hobgoblin, they are obviously Fey, like a Leprechaun is. It is actually the Elf and Gnome who should probably be recognized as Fey as well. If they arent Fey, this is an important design decision that requires thought, consistency, and emphasis. The design decision to place a creature in the playable species of the Humanoid type is something that players need to clearly understand.
It is always better to organize monsters by creature types. The alphabetic index belongs in the back of the book.
I know my humanoids can have different creature types depending on what plane they originate from.
D&D 4e distinguished between "creature type" and "planar origin". I find this helpful.
For the Humanoid type, add the planar origin as tags. "Humanoid (Fey)".