For many years, I played with DM's who rolled secretly behind screens, and one DM who rolled openly. After a particularly harrowing encounter with pirates on the high seas, my roommate's character was left bleeding out. After the session, he was in a bad mood, and I asked him why.
"I don't get it. What am I doing wrong? It feels like every battle, I go down, no matter how much I build up my AC."
"Well, what is your AC anyways?" I asked.
He told me, and I engaged in a thought experiment, crunching the numbers to try and figure out what the enemy's stats likely were. I quickly realized, however, that something was very wrong.
Either A, the pirates were way stronger than anything we should be fighting, or B, the DM had rolled nothing lower than a 17 every time he attacked my friend! The next session, I did some investigating in game- did the pirates have masterwork or magical weapons? Were there any spellcasters, like maybe Clerics with bless or Bards who could have granted bonuses to the group?
The DM, apparently thinking that I was looking for better treasure, was like "haha, no, they were all level 2 Warriors, that's all." And he showed me their stat blocks.
I was floored. Instead of being highly optimized or powerful NPC's, none of these guys had any real chance of hitting my roommate's character, let alone taking him to 0 hit points!
The DM had fudged his rolls the entire encounter, gleefully "critting" people simply based on his whims of how deadly the encounter should be. Suddenly, every time an enemy "hit" one of us, made a saving throw, or we "missed" an attack, I knew that the numbers didn't matter, our character builds didn't matter- the entire game was based on DM fiat.
I had a talk with the DM I knew that rolled openly, and he admitted that this is very common behavior. Many DM's, he claimed, have no real idea how to balance encounters, as the guidelines are often terrible. So they select monsters but adjust difficulty on the fly- if the enemy is too hard, you softball their attacks and damage. If too weak, the opposite.
I thought back to every time I had a DM ask me how many hit points I had left in battle, and I was dismayed to realize what they were really asking was "am I about to kill your character?".
I lost all my trust in DM's who rolled behind the screen for awhile. I realize that sometimes, yes, fudging might be necessary to keep your game running smoothly- it is hard to build an appropriate encounter. I usually find my encounters end up much harder or easier than I think they'll be, because there's a lot of factors involved, and the swinginess of die rolls doesn't really help matters.
What I decided to do, however, from that moment, is stop using a DM screen entirely. Yes, I was inviting disaster by "letting the dice fall where they may", but ultimately, I felt that this was a necessary concession, so that my players would know they can trust me to be fair. I embraced being as transparent as I could be- for awhile, I would let my players make checks to learn pretty much everything they wanted to know about a creature, inspired by 4e and Pathfinder- though since then, I've learned that players can only retain so much information, lol, so I usually only provide information if the player asks me outright, or it would be fairly obvious in-universe- the enemy was easy to hit, or it took less damage than expected.
I answered yes, DM's should roll openly, but I will concede that each group is different, and that it is entirely possible that an individual game could be improved by having secret information. But for me, I'd rather have less barriers between me and my players, because I find that the transparency greatly facilitates everyone having fun at the table. The players know I'm neither a control freak or out to get them, and thus I earn some goodwill for when encounters I've designed go drastically wrong, lol.
Ultimately, though, I've found there's something more important to the player/GM relationship than rolling dice openly or not. Being able to admit your mistakes. Yes, I overtuned that encounter. Yes, my ruling on a spell/ability/corner case wasn't ideal.
I made a mistake, and I'll do better in the future. I'm a hack DM who sometimes focuses on the wrong things. I've seen many DM's who refuse to admit they are wrong left wondering why their games implode or they start hemorrhaging players. And just being able to admit you're not perfect has gotten people back to the table more often than anything else.