The CW/DC universe has so far been unafraid to start dealing with alternate Earth versions of its characters -- especially Flash, with its regular sojourns to Earth-2. But even though Supergirl is already set on an alternate Earth, it has no plans to reveal its own takes on Barry, Ollie or anyone else any time soon.
Speaking to IGN, producer Andrew Kreisberg revealed that while Supergirl is more than fine with dealing with a lot of comic book shenanigans, the step of introducing Earth-38 versions of characters we've seen on Flash, Arrow and Legends of Tomorrow is a step too far for the show at the minute. Not because it's a particularly crazy idea, but if you introduce Earth-38 Barry Allen, you have to introduce all of them at some point:
The problem with that is it feels to us like if we do that once, we're going to open the floodgates of insanity. It's like Supergirl's over here, and it's its own show. Technically speaking, it's just another Earth, the same way Earth-2 is or Earth-3 or Earth-19. So technically speaking, there should be an Alex Danvers on Earth-1, or Earth Prime. But if we start doing that, I just feel like… Not that all hell hasn't broken loose already, but unless we had a really good story for it...
Which makes sense, really. Supergirl already has a lot on its plate, and the thought of wondering what its Earth's Oliver Queen or Sara Lance is like on top of it all is a bit much to contemplate. Plus, now that Kara has easy access to Earth-1, it'd be more fun to see her rubbing shoulders with the versions we know and love rather than Earth-38 characters who might end up being radically different. Maybe, like, I don't know, Oliver Queen of Earth-38 is a gardening-obsessed accountant. Not exactly a team up of the world's finest that, is it? (My apologies to any accountants, gardening fans or a mixture of both.)
For now, it's probably for the best that we stick to the incarnations of these characters that we're familiar with -- although Flash and Arrow have proven that, with the right character, you can do some pretty interesting stories with these alternate incarnations. That said, if Earth-1 or Earth-2 have a version of Mon-El hanging around that's a little less annoyingly perfect, I wouldn't mind Supergirl borrowing him for a bit.