LaidbackOne
Scrubby nice guy
In the new games he is called the Doomslayer and Doom Eternal comes out next year.I could see this, I suppose, but the fact that the character doesn't have an actual name besides 'Doomguy' (a little goofy) feels like it'd undercut it. But it wouldn't be a terrible fit. As a crossover they could have him be someone fighting Netherrealm demons or something.
The bigger point against it is that the DOOM franchise doesn't seem to have anything new to cross-promote?