it is just constantly shouting "this is a game!" in a way that for me personally, prevents any immersion in the world they have created
Try Doom 2016 if you haven't already. You can turn off some of the arcardy elements in the "advanced" video settings.
Turning off that, crosshairs, certain HUD elements, adding film grain etc. makes it more cinematic...
I think there are two main groups of DOOM gamers. One group, who considered the original games to be more of a survivor horror experience - you are stuck in the middle of nowhere, with only a shotgun and hordes of monsters blocking your path. Try to survive with the limited amount of supplies you have. The second group is people who consider DOOM to be more of an arcade experience - you are not stuck with the demons, they are stuck with you.
The first group might not like Doom 2016 too much, but the second group would love it (and love mods such as Brutal Doom).
Its fast-paced dynamics are built-in. You don't hide, you charge, you shoot while running. You bring hell to knees at their own game with sheer firepower and brutality.
Unless, as you say, it is a "reverse survival horror" https://www.reddit.com/r/Doom/comments/ew1gfu/doom_is_a_surv...
In that line, I retrospectively see Doom 2016 as an interaction between two villains. Samuel Hayden, a well-mannered mastermind. And you no-talk all-action, resolving all with force, and ripping demons with your bare hands.