"But mom..."
"We have to get the groceries! Put your comics away!"

"Due to continuous retconning and a usually sliding timescale, sometimes it can be hard to decide on what is really canon in a fanfic set in the DC Universe. According to the PPC Manual, this has made most agents give up on it, but some still accept missions there." - Quote from here.

Meaning that is hard to determine what is canon, no what is badfic. (In fact, there's at least one mission for the Main DCU.) The major problem with the canon, is not if something is or isn't, is to try to figure out from which canon it comes from. Why? Fans tend to combine, confuse and fuse elements and facts from Live-Action Movies, Animated Movies, Animated Series, Live-Action Series, Elseworlds/What if?/Alternate timeline/universe comics and Mainstream comics in their fanfics, and badfics usually top it off with misleading Fanbrat speculative ramblings, which are almost always wrong. So, if you want to take on a DCU or MU badfic, no one is going to stop you, but it'll be a very challeging endeavor, that will probably require you to have some sort of encyclopaedia on your side to take on.

And that's why Shattered Sanity is the only one to ever take on a Main DC Universe badfic so far, and even then, she took only one.

Because I'm having a hard time imagining Metropolis in Middle-earth.

You see, most of the implausibility coming out from badfic crossovers involving the DCU or the MU, is because of badly used elements from those universes. Like Gotham City existing within the Fire Nation, and The Batman's indentity still being Bruce Wayne. Things like that are highly implausible in the Avatar-verse. And yes, what I just described, some else wrote it already.

So, in short, while almost everything is plausible within superhero continua, that doesn't mean that it is plausible in the other continuum it is crossed over with.