Them dealing with the entire universe is even more reason for it to apply to them. Green Lanterns spend a fair amount of time doing stuff on Earth too.
Most of their opponents (apart from the other Lanterns) don't care much about Earth so it doesn't factor as much.
So do Batman, Wonder Woman, Flash, Aquaman, Zatanna, Cyborg, Martian Manhunter, Blue Beetle, Firestorm, Swamp Thing, Raven, Starfire, Captain Atom and a gazillion other heroes. I barely ever see any of their stories being handicapped by the ridiculous need to bring in other heroes or even acknowledge they exist.
Superman schools most Batman/Wonder Woman/Flash/Aquaman/Teen Titans/whoever villains. Zatanna's and Captain Atom's might cause him problems though. Point is, there is a reason why only some of them make appearance in JL comics. Point is, a villain who can cause real trouble to Superman is someone like Luthor, Zod, Darkseid, Brainiac or the Anti-Monitor (or someone on their level). The rest, he can deal with rather easily.
Overall, I think the real issue is that these villains are meant to come back. Having Superman fight a villain of equal power means he has to trap them in the Phantom Zone or kill them. Such villains are too much for any other hero to fight solo. His rogues can be a JL level threat on the highest level. Few other heroes can claim that.
Superman is technically supposed to have a super intellect and is scientifically inclined. Batman is a good detective but he really shouldn't be required for Clark/Kal to call on to do his science thinking in Superman's own stories as being a good detective does not equate to being a brilliant scientist especially when it comes to Kryptonian technology.
A good scientist isn't necessarily a good detective. You don't see Einstein going to find serial killers. Also, I always figured that Superman wanted to keep the level of technology he has access to hidden from the public. Sharing it with fellow heroes is fine but if the public realized he has the power to make a mini-universe, there might be trouble. People might accuse him of manufacturing evidence or hypnotizing people into committing crimes to present himself as a hero. Can't have that. Not to mention that Batman has access to his own high tech stuff, not needing much of Kryptonian tech to function. Maybe the medical stuff or a training room but that's it.
Then just move her over to someone else's rogues' gallery, I don't need to see her showing up and Superman suddenly developing a weakness to electricity just so she isn't a total joke.
Good God! You only read half the things I say. Superman might not be killed by her voltage but he can get stunned. He is very resistant, not immune. At the same time, Livewire is an excellent Superman villain. Sure, she can't kill Superman but she can cause black-outs or kill others. She has a lot of hostages at any given point of time and that makes her a good threat.
By that measure nobody is really an A-lister in the DC crew save for Bats and Supes.
Every core member of the JL that has its own famous Rogue's Gallery is an A-lister. The more famous sidekicks are too.
So you agree with what I'm saying in which case I don't understand what your point is other than perhaps trying to get the last word in.
I agree with some things and disagree with others. We are having a dialogue but you seem to be taking it as an attack.