Reducing LittleFinger to poverty doesn't end his storyline, he's clever enough to rise back up. The difference between Littlefinger and Varys is that Varys wants peace in the world and works to make it happen (while protecting himself) whereas Littlefinger wants himself at the top of the world and works to make it happen. He doesn't give a damn, ends justify means in every situation for Littlefinger. Even with the daughter of the woman he loved, he handed her over without issue.
Littlefinger's selfishness/cunning will be his demise. And it must be a death that immediately follows a successful move on the chess table. Littlefinger needs to have an arrogant moment in front of a crowd, giving one of his smug speeches about how he knew and planned for some type of victory, then it needs to turn on him and he needs to be given only long enough to realize all of his political maneuvering was for naught.
And we need to see him alone and cold and then death becomes him.
That's the only way I can see him getting his due process but since it's GRRM, he'll probably rule the North, make a terrible tactical decision that works in his favor against the Night king, and be revered in history as Azor Ahai for ever and ever. amen.