Soooo, um, can I just ask for final clarification from those who disagree with secret rolling. If you had a DM who you trusted who wanted to do secret rolling with you for something in particular, no funny business and was even willing to take photos of the rolls for you to see later, would you outright refuse to play, or just kind of grumble about it a little and give it a try? The goal of the DM was purely to try and enhance emersion in his own way.
No, I would not play like this. I have to add: anymore.
I feel that it is not the DMs responsibility to enhance my immersion by rolling dice for me because I am (and any player IMO) responsible for my own immersion. So if I have a problem with immersion, it is foremost my problem. Also, what I am getting out of this thread is that a lot of people use the secret rolls in exactly the way I use the Passive Perception/Passive Insight mechanic. Which has been around for many many years. Why people do not use this mechanic, I do not know. It's there and it solves much of the "metagaming" problem without the need to roll any dice.
Plus, it seems to me (I might be wrong about that, though) that those who argue for secret rolls in this thread do not use the "fail forward" approach or let the players succeed with a drawback. But this stuff is in the rules of the game and has also been around for many years.
And last but not least, I find the notion that a trained specialist can never be sure about the existence of traps, at least mechanical traps, utterly unbelievable. This gets even weirder with rogues of a high or very high level IMO.
Now, 30 years ago, when I did not know any better and these mechanics did not exist (at least not to my knowledge), I was fine with playing like this (and I did). But once mechanics that solved the perceived problem of "metagaming" (with which I do not have a problem to the same extent as others seem to have) had been created, I used and loved them. Especially because now they have been part of the D&D chassis for years. For years! So still rolling secret rolls in 2015 feels like taking away some of the rules because of what.... tradition? Argumentum ad antiquitatem, anyone? That is not enough for me, sorry.
What bothers me most, as I have said in the beginning of this thread, is that I (as a DM or player) believe that any player has the right to own that roll of the die. It is part of the action resolution and of the PCs action and directly connected to the PC. And I do not think any DM should take that away, however benevolent the DM might feel.
So all of this boils down to the fact that somebody who proposes this does not seem to be on the same page with me, if he or she insists on playing with that homebrew rule.
But let me ask you a question: If you are the DM and you want to play that way and roll secretely but the other players do not want you to but want to roll for themselves and actually see the result (and you know they would not "metagame") - would you DM for that group?
If somebody asked me to DM and roll secret rolls for them, I know I would refuse and not DM for that group if they insisted on this.