The first problem you will encounter when researching difficulty curves
 is how they are used exchangeably with (plain) difficulty.
For example:
    Youtube title "20 Recent Games With The HARSHEST DIFFICULTY CURVES"
    Article title "Best Games With High Difficulty Curves"
    Youtube title "3 Difficulty Curve Mistakes I Made In Game Development "
  where the authors really just meant "hard games".

Then, the graphs come:
 ▲    inc       dec       flat     a^b      wall
 d  │     .   │.        │        │    :   │      
    │   .'    │ '.      │......  │   :    │  :   
    │.:'      │   ':.   │        │..'     │..:   
 t▶ ┼──────   ┼──────   ┼──────  ┼──────  ┼──────
    > Difficulty(t)
    > where t is a snapshot of the game, commonly abstracted away as time for simplicity.
And even tho it looks like information from afar,
 all of this is meaningless.

The minute you present this to anyone with critical thinking skills,
 they will get confused as hell:
    https://www.youtube.com/watch?v=vWM_X1pC3oE&t=36752s

One problem is that we lack a definition for difficulty, it could be either:
    1. required resources
    2. required skill

---

The first definition is rarely spelled out explicitly as such, 
 but is the meaning derived from the idea that games should contain power-scaling.
This is what you will find articles in part describing implicitly,
 where having a curve is a good thing.

Lets plot it:
    Dark Souls 3    Witcher 3
    ▲              ▲    :
    │              │   .'  
    │              │   :   
    │      ..      │  :
    │..--''        │.'
    ┼───────▶      ┼───────▶

Well, we got curves, but there is very little we can tell from this.

You would think, that this atleast indicates how a low level character
 can kill high level enemies, however your brain is meta-gaming, actually.
Given that you do not know anything about the games,
 you would not know that there is progression systems involved.

To hammer home the point further,
 consider the difficulty curve of my imaginary game:
   Curve Stomper
    ▲               
    │   .----
    │   :           
    │   :           
    │.--'
    ┼───────▶
Seemingly, it contains, what would be referred to as a "brick wall",
 however, the player actually gains the "Fuck you, I win gun" right beforehand,
 so its a nothing burger.

If you noticed, I keep circling back to the notion of progression.
Fact of the matter is, the above definition *is* useful,
 given that there is no character progression,
 then the required skill level follows the challenge axes
 and we can actually use our graph.

Ok, so, this thing is clearly not what we want, because its not generally expressive.
Still, it doesn't stop people from using it:
    Anatomy of game design - Tom Smith
    https://davetech.davetech.co.uk/difficultycurves
    https://www.youtube.com/watch?v=GCQiktmq9T0