One thing that I think may not be obvious is that it may not be taking Alex all those seconds to come up with the answers, but he may be using every precious second before he answers to make sure that he has the right answer. Sometimes a contestant will blurt out an incorrect response to a Daily Double and then realize that they failed to read the clue properly or double check to make sure that their answer fit what the clue was asking. Alex is very cautious on this, taking all the time allowable for DDs and making sure that he is giving either the answer that he knows is correct, or his best possible educated guess. I understand that this may not make for the most pleasing game to watch because there is a lot of dead air while he is thinking, but he's obviously doing what he thinks gives him the best chance to win, so it's hard to fault him for that.
It's not uncommon for people to take this thinking time on DDs, but Alex definitely seems to be doing it at times on regular clues. We rarely see that, but it's certainly not something that he should be faulted for. Lots of answers that would probably come to him in a half second sitting on his couch may be a bit slower to materialize while standing there in the studio under the lights, wearing makeup, in front of a live audience, etc. It has been said by many that the actual physical exhaustion of a player after playing 5 games of Jeopardy in a single day is immense. There are so many great champions that won somewhere between 6 and 8 games and eventually lost, usually to a much lesser player, and the exhaustion factor has undoubtedly been a factor in many of these cases, even if it is impossible to know how much.
There is just no way to play your A game every single time out, game after game, and avoid making that one critical mistake that could cause your run to come to an end. It is a grind both mentally and physically, and probably emotionally as well for many players. This may be why Alex appears to not be showing any emotions throughout his games, he is trying to maintain a sense of calmness that allows him to play his best possible Jeopardy!, knowing that he doesn't want to get frazzled or frustrated or otherwise thrown off his game. It's been said by many that Ken Jennings was just a freak of nature, as the sense of exhaustion that every other multi-day champion seemed to run into in their inevitable undoing was simply not a factor for Ken. Julia probably had some of this quality as well, as she definitely exuded a sense of serene calmness throughout her 20 wins, while also managing to not appear as unemotional as many have called Alex.
I agree that Alex Trebek should have prompted him on the Ark response, but I think there is roughly a 1% chance that he would not have filled in Ark of the Covenant if required.