While I'm not fond of Doom 2016 I like Metroid Prime even less, so in theory, I could see this working in the sense of Prime 4 taking Doom's strengths while improving on its weaknesses. Such as:
-Movement: Prime absolutely botched Samus's sense of movement, least in comparison to the 2D games. There, Samus is quick, nimble, and agile. In Prime, Samus feels like a walking tank. If Samus moves like the Doom Slayer, then that could rectify that.
-Lore: In of itself, Doom 2016's lore isn't bad, it's just presented terribly, at least some of which comes off as being written on the fly. That said, the mechanics of the lore are far preferable to the scanning mechanic. From what I understand, AM2R does something similar, where lore is automatically unlocked once areas are entered. So Prime 4 could do something like Doom 2016 where codex entries are automatically granted as optional reading upon entering certain areas or killing certain foes. Just make it better written and more cohesive.
-Weapon System: Doom 2016's weapon wheel is a bit of genius. Just replace guns with arm cannon modes and voila.
Now, what Prime shouldn't do is:
-Tone: Obstensibly, Metroid is about isolation. Doom 2016 most certainly isn't - the Doom Slayer isn't Samus, and Samus shouldn't be presented as a psychopath that gets off killing monsters or Space Pirates. You can keep the mechanics of Doom 2016 without the tone coming through.
-Gameplay Loop: When there's combat, make it like 2016, but don't keep the whole hell portal nonsense. There's a sense of artificiality that pervades Doom 2016 when this happens, and it gets very old very quickly. In theory, Prime 4 should be less combat orientated, even if the combat itself remains hectic.