I assume it has something to do with the fact that literally none of the DLC third party outfits introduced in Smash 4 (Geno, Lloyd, Heihachi, Monster Hunter, etc) were given the upgrade treatment in all of Ultimate (unlike say, K. Rool, Chrom, Isabelle and Inkling in the base game).
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All of that could be explained though;
Geno - May not be a significant enough Mario character and definitely not a significant Square-Enix character.
Lloyd - Tales may be a long running RPG series but it's definitely below the likes of Tekken and Soul Calibur in both popularity and as Namco's top series.
Heihachi - Already explained that Kazuya had more moveset potential for Smash. As I mentioned above, Tekken is a very huge series, so it's really no surprise that it became the next Namco series to be represented after Pac-Man. If anything, that kind of adds to what I was saying about the significance of a series that's being represented.
Monster Hunter - Actually had a boss rep in Ultimate. Though in the end, that series also has to contend with other big hit Capcom series like Ghosts n' Goblins and Devil May Cry (both which have been around longer), so I wouldn't be surprised if Arthur and Dante got upgraded to playable characters before Monster Hunter.
I don't see any FPS rep as likely due to the genre's nonexistence on the Japanese market.
If that was the case, they wouldn't have even bothered with a Mii costume at all. Besides, Doom actually does have a fanbase in Japan, so it does have some recognition. Even Sakurai acknowledges how significant it is to video games.
In the end, it's that history that Sakurai is looking for and Doom has plenty of that.
I'm seen some people act like doomsayers, claiming that if a third party character becomes a Mii costume, then they're stuck that way forever. Two examples (Smash 4 and Smash Ultimate) isn't a pattern, and yet some people act like it's permanent and the developers will never change their minds and leave characters that were explicitly stated to be fan favourites as Mii costumes in all future Smash games.
I can understand if this pattern was used for one game but definitely not for the rest of the series. Kazuya alone should have been enough to show that a third-party series can indeed go from being represented by a Mii costume in one game to being represented by a playable character in the next and in the case of Doom, there's no better rep for the series than Doom Slayer himself.