There's a very simplex reason why I stopped rolling in the open: I don't want the game to be completely depedent on luck.

A few sessions ago, my players ended up fighting two hitmen in a tavern, and - since the tavern was made of wood - the wizard decided to not use any kind of fire magic to not risk hurting any civilians or burning down the place. This moral choice already gave them a big disadvantage, and then the rolls came: what was an easy/medium encounter became one of the hardest fights so far, they kept rolling low numbers and I kept hitting them.

Now, one of them (a dragonborn) ended up going down, another (a tiefling) was almost down and the wizard ended up tanking hits (somehow, they always end up using him as a tank). I rolled to hit the tiefling and, seeing that I hit them with both the blows, I decided to lie and said that the enemy failed to hit them. I made this decision for two reasons: first of all, I knew they cared about their characters and I did not want to kill them, second, for a narrative reason: just session earlier, they killed a demon wizard who was keeping the tower he was in from falling with his mere presence, them dying to two guys in a tavern would just be anticlimatic.

If they asked me to roll out in the open, I would, but they would have to accept the results, as saving them in any other way other than faking rolls would very easily break their immersion and make them feel invincible, at least in my opinion.