Personally I thought that Doom '16 did feel like the developers had a good amount of experience with classic Doom, but it is clear that there were some design decisions like the linear level design that were most likely used to capture a modern audience, since linear levels make up the majority of big name shooters nowadays. I would like to see some more interesting encounters, I felt that near the end the game stagnated a bit and why it's hard for me to go back to Doom '16 and also what killed Doom 3 for me, although in 3 it was much worse in my opinion.
Although taking something as broad as all the flaws in Doom '16 and trying to compare Doom or Doom 2 seems like way too much for a single thread.