No one was charge because of simple expediency in that Lincoln felt it would only make matters worse for a nation sick of the bloodiest war in our nations history. A war by the way the SOUTH provoked and started!
Lee and Davis should have considered themselves lucky indeed they weren’t hung.
The South simply wished to be left to do as they wished.
Lincoln started the war. Deliberately, and with malice aforethought. He thought it would be a picnic, and it turned horrible much to his shock and dismay.
The South had a moral and legal right to leave the nation. Lincoln had no legal or moral right to stop them.
Lee and Davis were not hung because what they did was not treason. Nobody was hung for leaving. The only people hung were hung for crimes of war and regular crimes. No one was hung for treason because leaving is not treason.
If it were "treason", nobody could immigrate to another country. People can give up their citizenship if they want. They have that right.
You may not like it, but it is true. People can give up their American citizenship, and some do.