One of the few things ASF did well was to make Bison look like a legitimate threat to the world.
In the various games, anime, movies, etc Bison has always had weird and/or nebulous plans. He holds a martial arts tournament. He’s kidnapping and brainwashing martial artists. He has clone bodies and resurrection plans. He heads a worldwide criminal empire that is doing regular criminal empire stuff for regular criminal empire reasons. When he does attempt something bigger than just kidnapping or beating up some martial artists, he gets stopped before he can even really get started.
In ASF, his plan is arguably sillier than ever. He is also, as ever, defeated. The difference is in the details. The silliness is somewhat alleviated by it being FANG’s operation; Bison’s own goal is brutally straightforward and even logical for him. He is defeated, but here he isn’t angry, panicked, or vindictive. He simply stands tall and laughs as his body is destroyed. While his ultimate goal remains increasing his personal power, he’s now operating at a worldwide threat level instead of threatening a handful of individuals.
And Bison succeeds at throwing the world into chaos. Barring Capcom simply ignoring the consequences or retconning ASF, Bison has scarred humanity at large. People aren’t just going to forget mysterious metal spheres appearing over major cities, setting off EMP blasts that turn a night sky into day. That’s without even getting into both immediate and long term injuries and fatalities. Even if you wanted to be optimistic, fatalities would still be counted in the thousands. Pessimistically, the long term fatalities could potentially be counted in the millions.
Of course this does leave Bison in a position where a future return will very likely only weaken him. After all, where could he go from here? He “won”, and yet still lost to Ryu. He seemingly accepted defeat, even if he expected to return. He can’t go bigger than worldwide terror, but just trying to steal Ryu’s body again at this point is going to bring him right back down to Akuma or Kage’s level.
At this point, Bison might best be served by staying a never realized background threat as others fully take center stage. The idea of Bison’s return itself is enough to work as a B-plot for Neo Shadaloo. While not to the degree of Seth’s madness, characters like Ed and Falke will be under the shadow of Bison’s return, and affected by the risk of Bison’s return, even if Bison makes no actual effort to return. Similar goes for F.A.N.G (if he survived) or anyone that tries to follow in F.A.N.G’s footsteps, who will either start prepping for Bison’s return or directly attempting to accelerate Bison’s return. Just don’t have Bison himself actually attempting to return. (If BIson attempts to return and fails, that’s just another Bison appearance that led to pointless failure. If Bison attempts to return and succeeds, that just distracts from the other stories you are hopefully trying to tell.) Save that for the future.