Last things first. It should not be off-limits. And the person making the charge shouldn't be surprised when he gets pushback.
When prosecution for treason was considered after the war, there were all kinds of legal technicalities advanced as reasons not to have a trial. Most of them weren't very convincing. There was no trial because of the political awkwardness. It would have kept the country divided and a jury's verdict couldn't have been reliably predicted.
What were the technicalities? I'm aware that Chief Justice Salmon Chase warned the administration of the possibility of losing on constitutional grounds, but I'm not convinced that a jury couldn't have been cherry-picked, even in Virginia. Davis was hardly more popular in Virginia than in the North by the end of the war. The administration certainly had no problem getting a Virginia grand jury to indict him in the first place.
I can't say how valid it is. If it's true, the arguments seem pretty slippery.
Finding a jury in Virginia wouldn't have been impossible, but as a unanimous verdict was required, you could never be sure there wouldn't be one joker in the deck.