what is the design principle that explain there is no creature with multiple creature type

This question bothers me. Why can't creatures have multiple creature types ? Why a dracoliche doesn't have the dragon and undead creature type, or the hellish fire giant in the Bigby book isn't a giant and fiend (devil) ? I believe it was released in an Unearthed Arcana about playable races (for ravenloft) but I can't find any example for monsters.

I assume this is a complexity issue, it could make designing future features that involve creature type harder, or constraint the wording of features too much.

My question is, is there a thing I am missing about creatures with multiple types that makes it impossible to do (if I were to homebrew such a monster, would it break the game ?).

And additionally, is this a design principle ? D&D use a "typal" system (there are types with no rules associated, and rules that refer to those types) where most things (monsters, feats, damage) have only one type. By opposition MtG uses a similar system but with combination of types

It keeps things simpler and avoids arguments. The first example I can think of is a spell like hold person. It only affects humanoids. If you have some kind of elf-tiger hybrid and give it both the humanoid and beast types, does hold person work because of the humanoid or does it not work because of the beast? Can a spores Druid turn them into one of their little followers?

Or your dragon/undead example, can a cleric turn because it’s undead, or not because it’s a dragon? Would a paladin smite get the extra damage vs undead or no? Does a dragon’s bane weapon do extra damage? Does a paladin smiting with a dragon’s bane weapon get all the bonuses or none or just one or the other? And how to you apply something like that consistently?

So I don’t know if making one would necessarily be game breaking, but it would create some edge cases. And it could actually make some creatures weaker or stronger as they’d be subject to multiple sets effects, depending on how you run it.

I don't think there's any particular reason, it's just how they've decided to design the game.  The type is sort of part of a creature's identity -- it's how they are categorized.  Like, in real life we have the system of Kingdom, Phylum, Class, etc.  As far as I know there is no living thing that is officially categorized as both a Plant and an Animal, for example.  One or the other is chosen and that's just how that thing becomes categorized.

In addition to creature type, a creature can also have descriptive tags, of which there could be more than one.

From the Monster Manual:

Each monster has a tag that identifies the type of creature it is. Certain spells, magic items, class features, and other effects in the game interact in special ways with creatures of a particular type.

A monster might have one or more tags in parentheses following its type. Such tags provide additional categorization and have no rules of their own, but certain game effects might refer to them.