When it comes to Superman, WB hasn't pleased the casuals either or else the movie version would have been more embraced and actually be continuing. They have to earn back everyone's trust with the brand, and there is no guarantee they will do right by Kara either. Casual audiences will go see Supergirl and not care about the use of Brainiac if the movie is good, but if WB is seriously planning to replace Clark with Kara completely and not show the two cousins interacting, even the casuals are gonna feel serious gypped and regard it as the transparent shitty story telling that it is. If the films don't care enough about the familial connection to show the characters interacting, why should the audience?
Yes, it's almost as if...she's a spin-off character made two decades after the main character to appeal to a female audience, and not an individual property herself and rides on the association with him to launch to success! Complete with her own gender swapped versions of Lana Lang and Lori Lemaris.
It seems more like a big deal to Superman fans in the current era of superhero movies that the most they get is one very divisive and flawed solo movie in which he isn't even a fully formed Superman and rehashes his origin yet again, a sequel with all his screen time cut that was hijacked by Batman and barely interacts with his arch nemesis, and 10 minutes with CGI lips in the godawful JL, and are now not getting anything else. On top of the earlier lack luster franchise launcher Superman Returns. And now rumors are framing this as WB not even needing him anymore and giving everything to Kara, while being more prepared to give Batman yet another shot after DCEU Bats wasn't any more well received and he already had the Nolan trilogy.
Meanwhile, Captain America gets a trilogy to himself as the lead and many successful co-lead roles in team up movies, and even if he's bowing out soon he was VERY well received and they can carry on with his own properly set up and popular spin off character, Bucky. And Steve and Bucky actually got to interact on screen to get people to give a crap, while Clark and Kara may not get the same treatment.