There's nothing to indicate in any of the rules that anyone, player or DM, hide rolls.
DnD 5e DMG pg 235 "Rolling behind the screen lets you fudge the results if you want to If two critical hits in a row would kill a character, you could change the second critical hit into a normal hit, or even a miss, Dont distort die rolls too often, though, and don't let on that your doing it. Otherwise your players might think they dont face any real risks-- or worse, that you're playing favorites."
Page 237, 5E DMG "Remember that dice don't run your game - you do. Dice are like rules. They're tools to help keep the action moving."
If I weren't good with things being determined by die rolls (good/bd/otherwise) I wouldn't roll to begin with.
You're missing the point of showmanship.
Sometimes it's entirely appropriate to roll some dice, ignore the result, pretend to look something up, put a worried look on your face, and sigh while slowly shaking your head from side to side.
I'll have 'random' encounters that arent (they were planned from the beginning). The 'roll to trigger them' simply keeps the players guessing.
Other times, I'll roll some dice just to quiet table talk, and get the players focussed back on the task at hand.
Other times, it's simply to keep the players guessing -what- exactly I'm rolling for.
That's all simple showmanship and entertainment - keeping the session fun and engaging for the players. You're using the dice as as prop. It's a tool in my arsenal and I see no reason not to use it.
Im also not a fan of having PCs die for no other reason than a series of bad dice rolls. That said, quite often I'll throw the dice down in the middle of the table and let them fall where they may.
When I do that, all eyes are on the dice.
Dice are more than just random number generators, just like DMs are more than just addition machines. They're a powerful tool for engagement, enjoyment and storytelling purposes, and a DM is there to do more than just roll them to determine a number.
Technically I roll in the open.
I haven't used a screen in 20+ years, & my dice are bright yellow with black #s. Very easy to read (& chosen for MY convenience).
Typically I roll my dice only as far as my arm can reach while seated. Now & then I'll roll near where the minis are if I'm moving things about, but not often (I'm lazy & just tell the nearest player where to move model x)
However.... Tables either 6x4 or 8x4 depending upon where we're playing, & I sit at one end of it.
So the people on my immediate L/R can see my rolls (if they care). The others? I guess it depends upon how good their eyes are & if they care. No ones ever stood up to check.
I roll in the open because it supports a principle of DMing that I hold which is that the players should never have a reason to doubt the honesty of the DM.
It's not his honesty they should never have reason to doubt. It's his commitment to being fair, reasonable, knowledgeable and entertaining.
Those two things are not the same.