Atom don't take on Superman (but you did see Sivana take on both Supermen and Captain Marvel pre-Crisis), Monster Society of Evil taking on the Secret Society of Villains with the JLA/JSA/Crime Crusaders caught in the middle. You don't see a cross pollination of villains: Sivana or Mr. The Freedom Fighters who were still young in COIE are now old and giving way to legacy characters and then more legacy characters. Suddenly, Captain Marvel is part of a continuity heavy universe and has his villains and friends heavily changed. If anything, I think trying to force everything into one continuity ended up being detrimental. In fact books devoted to the alternate earth characters didn't long survive the change-over. Other than the push of the Charlton characters which would have happened one way or another (and could have been brought in as having always been part of Earth 1, their adventures just occurred off panel for the readers), not much more was really done with the alternate earth characters than had been before. So, instead of more Alan Scott, Jay Garrick appearing in their alternate books without having to contrive crossing earths, you got less! Characters that were the top heroes of their world were played as being second fiddle to Superman, Batman, etc. One of the first steps they did was get rid of the JSA, the biggest alternate earth guns they had. That could mean either that they grow up to stand on their own legs, or, what I think more likely, they have eventually faded into obscurity.That's part of the problem though.
It means that minor characters, or character from other companies, are still locked within their own universes, and don't interact with Supes, Batman or Wonder Woman on a steady basis.