I totally agree. I think it comes down to "show, don't tell", basically. In Doom and Doom II, you feel like a badass because you're mowing down tons of powerful demons singlehandedly. That was more than enough. Eternal and Dark Ages feel the need to constantly tell the player what a badass the Doom Slayer is, and it feels forced.
I think you are really selling 2016 short here. Almost every big FPS at the time was a shooting gallery. Walk into an area, enemies spawn, shoot them until your screen turns red, hide behind a wall until the red disappears, continue. People always say that Doom 2016 went back to its roots, but I don't think that's really true. It was a total paradigm shift. Instead of shooting from a distance and hiding while your health regenerated, you had to push foward into the enemies, doing glory kills to recover health. You chainsaw enemies to recover your ammo. You're literally chasing enemies down. It was a complete inversion of the genre. Glory kills aren't just a neat flourish, they're the concept the whole game revolves around and what separated it from other shooters, including the other Dooms.
That said, probably my biggest complaint of 2016 is that the game is too long. I think they could have shortened it up for a tighter, better experience.