Purpose of cessation or Nirvana! What is the purpose or cause of cessation or extinction or Nirvana. Did Buddha ever talk about it?
For example, see how SN 23.1 ends:

“But sir, what is the purpose of extinguishment?”
“Your question goes too far, Rādha. You couldn’t figure out the limit of questions. For extinguishment is the culmination, destination, and end of the spiritual life.”
So Radha is asking kimatthiya --

“But sir, what is the purpose of extinguishment?”
“Nibbānaṃ pana, bhante, kimatthiyan”ti?

That is kim plus atthiya
So asking &quot;kimatthiya?&quot; is like asking, &quot;Nibbana is with the intention of satisfying a desire for what beyond nibbana?&quot;
The question implies that nibbana is a stepping-stone to something else -- like a way of getting from here to somewhere else.
But it isn't -- instead it's the destination, the end-result, the goal.
I think that's explained in the Uṇṇābhabrāhmaṇa Sutta (SN 51.15)

“The purpose of living the spiritual life under the Buddha, brahmin, is to give up desire.”
“But is there a path and a practice for giving up that desire?”
“There is.”
“What is that path?”
“It’s when a mendicant develops the basis of psychic power that has immersion due to enthusiasm … energy … mental development … inquiry, and active effort. This is the path and the practice for giving up that desire.”
“This being the case, Master Ānanda, the path is endless, not finite. For it’s not possible to give up desire by means of desire.”
“Well then, brahmin, I’ll ask you about this in return, and you can answer as you like. What do you think, brahmin? Have you ever had a desire to walk to the park, but when you arrived at the park, the corresponding desire faded away?”
“Yes, sir.”