DC didnt able to handle it. First they sended all of these heroes to Earth-2 then come back again, then send again its a mess.
But ı think these team could co-exist with JLA. Or even cross-over with in .
JLA is more about cosmic and technological threats and big stories.
But JSA Could deal with mystic powerhouses, phenomenons all over the galaxy.
And both teams should leave the "America" part of their title.
Justice League is enough and for JSA JS is enough or Justice Society of Galaxy.
JSA shouldnt be big as JLA. This is more special, traditional and compact group
Doctor Fate (not should be hanging out with JSA all time cuz he is the agent of Order for all Prime-Earth universe but for special occasions he rejoins)
Dr. Mid-nite (huge potential)
Citizen Steel (or Commander Steel but Citizen is better)
Manhunter (Kate Spencer)
Sandman (not the endless one)
Ted Knight or Adam Strange
And thats it. The Team shouldnt contain anymore heroes than this.