Hiding Dice Rolls: Why and When

So this is more why I don't hide my roles. The header says fudging which you can say, just because you hide your rolls doesn't mean you fudge your dice rolls - yeah it does. Why else are they hidden then? If you use the roll you rolled no matter what, then why hide them? That seems like a weird ego/power trip.
So yeah. I roll in front of the players, I tell them the AC once they are able to figure it out even if they hadn't. Say a PC missed round 1 with a 12. Later round 3. Another PC rolled a 13 and hit. I'd describe it as hitting before telling the players the Monsters AC was/is 13. I tell them the save DC they have to roll against before the roll with the option of using bless or a bardic inspiration die even after they see they rolled too low, BUT they have to say if they will use it or not provided they do fail. (you'd be surprised how many still say "no I wanna save it"...) "But DM...y tho?" You're right... I'm not perfect, and should the players really be punished because I misgauged an encounter and now they got TPK'd...Yes, they should and I am aware of that happening. "Isn't the story told what matters most, tho aren't you always preaching how much you the story matters and being true to as realistic outcomes as possible?" ...well, yeah, but... "What gives, DM?" Alright, alright. Easy. We're here to play together and tell a story together. As the DM, you are already able to alter and change, on-the-fly you can even fuckin retcon if you so choose, all the while the players are at your mercy. Yours and the Dice. Rolling in front of the Players creates a sort of camaraderie you don't notice until you try both ways. It's a small way to show the players you're in this with them, and it also keeps you guilt-free and free from accusations. If you are hiding dice rolls and a character dies, no matter what you say or feel it died because you wanted them to die. Full stop. Think about that. Their character died because you willed it so. Whether or not you fudged that roll or not- well why didn't you? If you did, well wtf you're an asshole then. rly...y tho? Honestly, I am too new at DMing and I feel the trust from my players isn't at a level I feel comfortable being the arbiter. I simply am not experienced enough or at least confident that I know when and if a certain die roll needs fudging. I am forgetting legendary actions and class mechanics EVERY session. Can I really then decide that "I feel this crit should/n't happen "? I don't think so, personally