I'm not really sure I think every character should be on a team. But connections to a wider world can help drive stories. I don't really care for the JSA on the same earth as the JLA, but if they are, I guess than can work.
Although I wouldn't do it anyway, I can't really picture a group of formerly-Fawcett heroes all on a team, even if they were on their own earth. But I may have well said the same about DC heroes one upon a time - many also designed to inhabit their own worlds. And Billy had some crossovers even way back when.
Wait, does Ted Kord count there? I think he's firmly planted in the JLI now.we can cram all the 'originated on another Earth' on that team