Could we get a Superman show now that "Arrow" will be ending next year?

They have already introduced new characters, and there is no reason why the series couldn't create its own. In fact, it already has.

 

Over the course of four seasons, Supergirl has created and introduced a grand total of 7 completely original characters, only four of whom have been villainous.

Creating an entire Rogues Gallery for Kara would require a lot more time and effort than the producers and writers have to spare.

 

That's not entirely true. Series based on original characters do it all the time.

 

One of the reasons for the DCW shows to use pre-existing characters from the comics rather than create new ones, even if said pre-existing character isn't usually associated with the hero of the show, is to get around paying royalties to the writers.
TV writers get royalties for each appearance of a character they created. But studios like to look for ways to get around doing so, as was the case with Dennis Pearson, the ghost roommate of Cordelia on "Angel", created by Jane Espenson. The studio argued that Dennis was invisible, and therefore didn't make any appearance on the show, so they didn't have to pay Espenson.

The creators of the comics characters are supposed to be payed royalties, but with older characters it is sometimes hard to identify the creator of a character (like Jimmy Olsen, who first appeared on the Superman radio show before being introduced to the comics), and even with newer characters, the studio finds their creative justifications for not paying any royalties.
There was a case of this when The Flash started out and the studio didn't pay Killer Frost creator Gerry Conway for the use of Caitlin Snow, arguing that Caitlin Snow was a different Killer Frost than the one created by Gerry Conway (the original Killer Frost's name was Louise Lincoln), and the TV version was not Killer Frost at all (yet). On the other hand, they didn't pay royalties to Dan Jurgens, who created the Caitlin Snow version of Killer Frost, arguing she was a derivative version of the Killer Frost character created by Conway. So they argued one way to get out of paying one creator and the opposite way to get out of paying the other creator. Of course, I expect that changed since then, at least since Caitlin went full Killer Frost on the show.

Another reason, of course, for using pre-existing characters is to create buzz among the fan community.

 

Yes. Why not? Why not take the opportunity to give her a rogue gallery. Why not come up with new threats and challenges?

The producers/writers of Smallville came up with new villains and monsters for young Clark to battle, especially in their earlier seasons.

 

^ A bunch of one-off "Monster of the Week" characters do not constitute a Rogues Gallery, and developing a satisfactory repository of fully-fleshed-out villains for Kara to face that were unique to her and weren't just throwaway adversaries would have taken significantly more time and planning than is available to the writers and producers of the series.

 

I for one hope not! The last thing I want from the writing staff of my multiverse-traveling alien superhero program is an imagination!

 

I don't understand what this means. Can someone explain it to me?

There are quite a few entries on this page: https://dc.fandom.com/wiki/Supergirl_Villains.

 

Amen. I love the spooky corners of the DCU. See also Madame Xanadu, the Phantom Stranger, the Demon, Deadman, etc. Bring on the Justice League Dark.

Ooh, maybe we can get Man-Bat on BATWOMAN. Or, even better, a Woman-Bat?

 

I was a little surprised we haven't had an appearance by Zatanna on the current season of Legends of the Tomorrow. They're dealing with magic all season, and I believe in at least the New 52 her and Constantine have a history, so there are plenty of reasons she could have popped up.

 

Constantine and Zatanna have had a past since way before the New 52, so, yeah, it would make sense for her to show up on LEGENDS. They could have fun with her speaking backwards and all.