Sakurai has acknowledged John Carmack (who made DOOM), as the father of the FPS genre in the
Sakurai x Normura interview (Part 2). In the very same interview he acknowledges Castlevania, which would be included in Smash Ultimate. While Sakurai also mentioned many other game designers, it's important that Sakurai says this:
Internationally. Seems to fit in with this
other popular Sakurai statement from the Sm4sh DLC (read: Pre-Ultimate) era in regards to third parties.
DOOM could certainly be one of the few "major globally-recognized franchises" left at this point. I would even say it's likely this is the case. Given Nintendo and Bethesda's great relationship recently, and the fact that
Bethesda has spoken with Nintendo about Smash leads me to believe that it's likely that DOOM Guy was on Nintendo's list and Sakurai chose him as a hype third party pick.