With all due respect to DOOM, Doom Guy is just one of those third party characters that only really got serious traction in Smash circles because of DOOM 2016 and other Bethesda games being ported over to Switch. Same thing happened with Crash, who didn't really make it big until Crash N. Sane Trilogy was announced for Switch in the very same Direct Smash Ultimate was teased at.
DOOM 2016 absolutely did have an influence on Doomguy's support, you're not wrong; it was the rebirth of the franchise and brought DOOM back to the mainstream after a pretty long drought. And the fact it was ported to a Nintendo system, rekindling that seemingly previously-dormant relationship between id Software and Nintendo, definitely gave fans hope for more collaboration in the future (be it Smash or sequels, as has happened with Eternal).
But I think there's a bit more to it than that.
DOOM has had a history with Nintendo going all the way back to the SNES (id Software's relationship with them even further still, with the whole "Dangerous Dave in Copyright Infringement" thing), and had releases/ports up through the GBA era - even having a fully unique mainline installment on the N64 that was Nintendo-exclusive for over 20 years. Ever since third party reps. have been a possibility Doomguy has always had some degree of support for Smash, however small.
But the reasons it was never as vocal as it is now (as I see it) was more that there was (A) little overlap in its core community with Smash (and even still, there are those in the DOOM community who are actively
against him being in Smash) but mainly (B): The notion that M-rated regular gun-toting characters were pretty much forbidden or impossible in Smash for age ratings reasons.
Issue (A) was partially lessened by DOOM 2016 bringing in new fans of the series, some of whom may have gone back and learned its history and tried the older games, and seen the potential for a Smash inclusion.
And regarding (B), I think something that really added fuel to the possibility (and thus vocal support) of Doomguy in Smash was Bayonetta's inclusion in Smash 4 and more recently Joker's in Ultimate. Bayo especially due to her game's themes, but both featured previously-unseen degrees of gun "acceptance" (for lack of a better word) compared to other characters. Snake seemed to get away with his weaponry because they were all explosives, but now Joker can carry a regular-looking pistol (in-universe mechanics aside)? You can see how some would think the door's been opened somewhat. (Whether that's actually the case or not.)
I think Doomguy is one of those characters that if not for the age ratings concerns and lack of popularity overseas he would probably already have some sort of representation, be it a character or at least a Spirit event. id Software pioneered the FPS genre as we know it with DOOM being cited as the game that really kicked it off (it had predecessors of course), they've been longtime allies with Nintendo, and they've spoken multiple times about wanting Doomguy in Smash. It's a bit of a shame that rich history hasn't resulted in anything in Smash. (Though again, understandable given the aforementioned issues.)
