Really, DAvis ASKED for a trial. No one in Justice wanted to try him because that would put secession on trial and they thought they would LOSE.
That's a simplification.
We can get into an enormous debate, but the Supremacy Clause of the Constitution by its very nature rules out all unilateral secession.
Whether or not you believe that to be the case, James Speed (AG at the time of Davis' arrest) was 110% certain that it was the case and would have been more than happy to argue it.
That's why he indicted Davis for treason.
Davis fought the indictment, his lawyers seeking to have it quashed or nullified on the grounds that the court did not have authority over him.
This dragged on for four years.
After Davis lost his last appeal to have it quashed, the new Grant administration just took office and believed that starting the new administration with a trial that would reopen all the old wounds was just not smart.
I agree with that.
After the Grant administration dropped the case, which given the composition of the Supreme Court at that time would have gone 7-2 or 8-1 against Davis, Davis - now free and clear of any repercussions - started saying that he would want a trial.
Davis did not get himself elected President of the Confederacy by being a bad politician.