After retrieving the jagged crown, it's possible to bring it to the opposite faction. This doesn't trigger any hostile reaction by the individual NPCs involved (Tullius, Ulfric and their underlings) other than switching sides in the war with all the obvious consequences.

Who tried thIs and why?

I did once; I wanted to end the civil war in favor of the empire but I wanted to have my hands free from any oath sworn to the legion or such. Ah yes, I almost forgot: by giving the crown to the other side, you'll skip the joining ritual for the winning faction. Perfect for an ambitious dragonborn who is not content with becoming another underling of Ulfric or the Legion... I'm sure Hjalti would be proud of me

i didnt know this was possible, its a shame too i just completed this part of the quest and i kinda wanna switch over to stormcloak. is there any other point where you can switch sides? double crossing tullius would be pretty sweet imo