Interesting discussion. Unsurprisingly people that prefer different playstyles provide a different response to the original question.
(Mis)trust of players towards the GM has been named abundantly, but I must emphasize that to me this reason is not the primary one for preferring open die rolls. It is to live the tension of the die rolls by the GM. To see that 20 fall and realizing that my PC is going to take a crit from the giant. Some contend that the GM storytelling that crit is the same thing. I beg to differ, that die falling simply has the table roaring when the stakes are high in a unique manner. It's like watching a sports game. When the ball/puck enters the net, everyone jumps at the same time. When someone else watches the game and at some point tells you that the ball/puck entered the net, maybe their storytelling is good, but it will never be the same thing. The storytelling will come after the die roll anyway. Yesterday we had a great game, PC's were fighting a BBEG and at the end only the dragon was left. PC's were heavily battered, the mage was at 2 HP, the dragon goes against the mage in melee, and as GM I roll 3 attacks against the mage with the dragon and miss all three in a row. The players were cheering! The mage followed on his turn and dealt an unusually high amount of damage to the dragon and that led to victory about a round later. When did the players cheer most? When the dice fell.
On a different note, one thing that was not discussed yet regarding trust, since this topic seems to be the hot one here, is whether the GM trusts the players. By that I do not mean whether the GM believes the players fudge die rolls - they normally dont and can't since they roll in the open. It has been stated by many that fudging is sometimes desirable for the GM's intended outcome, but why not trust that the players will like the spur of the moment story twist of the unintended die roll?
Also, it has been stated as a reason for concealed die rolls that players should not be allowed some knowledge about their opponents. But, perhaps GMs could trust their players with the metagame knowledge gained from die rolls that fall on the table. Where it matters I trust my players to play to their character's knowledge and not to the player's. It has worked well for years. In the rare circumstances where they are not certain, they ask me: would my character know X? I often ask them back: do you think your character would know? I probably accept their decision close to 100% of the time. Even if I would have initially disagreed. This is cooperative storytelling, why would their reason not be as valid as mine?
Yet another point: trying to conceal monster stats is kind of pointless, but moreover it's fun that the players can gradually learn those stats as the battle goes on. Players will relatively quickly learn the creature's attack bonus, and so what? Does that break anything? Would the character not be able to recognize a competent opponent that attacks at +10 or an incompetent one that attacks at +4? It seems to me like the players learning it attacks at +10 is pretty equivalent to the characters learning that the creature is competent when they see it fight. I even call out the save bonuses of my opponents to my players before rolling their save. Does it break anything? Not in years of play it hasn't. They learn if a creature has a strength or weakness. They might take advantage of that knowledge which is tactically fun. If you roll behind your screen, do you ever let on any clue to the players of whether the opponent appears to be powerful or weak vs. any specific attack type? It's the same thing.
In summary for years now in different groups me and other GMs that I play with have rolled in the open, and we've trusted our players to use that knowledge in a way that is positive for the game, including ignoring knowledge where it seems more fun - the GM does that continuously, the players are very capable of doing it also, but this requires trust also. Where meta knowledge such as actual stats of the opponents provides players with a tactical advantage as the fight goes on it is just fun. As GM I like it that my players figure out that their opponent was mentally strong to resist enchantments but was not agile and had a harder time jumping out of a fireball. And in the end, it's great fun to see the dice fall and all cheer or boo at the same time.