They could have, but they didn't. Davis was held at Fortress Monroe headed for a military trial. The Johnson government decided that any trial for treason would have to be in a civil court in Virginia. Neither John C. Underwood, circuit court judge for the District of Virginia, nor Chief Justice Chase, who presided over the circuit including the Virginia district, felt that they had any authority over the case as long as Davis was held by the military. That didn't happen until May of 1867 when the writ was issued, Davis was arraigned and released on bail. The trial was delayed again for political reasons involved with the impeachment and the election. By the time the government was ready to proceed the 14th Amendment had been ratified.
Instead, they understood that to bring him to trial would validate secession.
How would trying and convicting Davis validate secession? A treason conviction would justify the administration's actions, not invalidate them.
How dense can you be? There was no trial for one reason and one reason only. The government would first have had to make the case that unilateral secession was forbiden under the Constitution. It was recognized that this would not be possible and exposing that fact would have opened an enormous can of worms. Apparently it was hoped that Davis and Stephans, who both appeared to be in frail health, would not survive their abominable conditions of incarceration. When it became apparent that they weren't going to die in the short term, there was nothing left to do but to relaese them.
Chase believed that the government could NOT convict Davis of treason - secession was not illegal.
4ConservativeJustices was obviously referring to the quote by Stanton to Chase, saying effectively that the Constitution does not equate secession with treason and, therefore, the Federal government couldn't convict Jefferson Davis.