I definitely don't misunderstand what swap is for. I've implemented swap for a hobby os.

Swap is absolutely "more RAM" in layman's terms. If you NEED 10GB of memory to have open everything you want on your machine, but you only have 8GB of RAM, swap will make that happen for you. Now ideally the OS is using this for inactive pages (those programs you have open but you aren't actually using), and the nuance to how swap can be used to make the RAM you do have more effective is an interesting attribute of swap (another commenter mentioned swap being used as temporary storage to defrag the physical memory), but every single reference you linked says the same thing - swap is for when you need more memory than you have physical memory for.

  > I definitely don't misunderstand what swap is for. 

  > Swap is absolutely "more RAM" in layman's terms.