Every Superman is brunette, Every Batman is brunette. Every single time.
I dont think anyone stated her popularity was in her hair color.
Exactly. Hair color does not define these characters' popularity. Hair color does, however, become part of these characters' iconic visual identities, especially if said identity has remained fairly consistent throughout the years, versions, and media.
Is Superman popular because he has dark hair? No. Of course not.
But has Superman consistently been depicted as having dark hair? Yes. Same with Batman. Same with Wonder Woman. Likewise, Kara Zor-El Supergirl has been consistently depicted as blonde. Not a readhead. Not a brunette. Not green or purple hair with a mohawk. Blonde.
True. The multiverse opens up the possibility of these classic characters having different looks (and personalities). And that's the one leeway or wiggle room this film has. So, if this Supergirl from an alternate universe ends up being a dark haired Supergirl, then so be it. Yes. I will be disappointed on some level. But I can accept that this is an alternate universe version of the character. I'm just glad we are getting Supergirl and something Superman related.
And again. All of this is pure premature speculation on all of our parts. For all we know, they'll simply dye the actress' hair blonde and this whole debate will be moot.
And she may not even be playing Kara Zor-El, cousin of Superman, version of Supergirl. As I said, she could be "Lara Kent" daughter of Superman and Lois (or Wonder Woman). In fact, having Keaton's old man Batman opens up the chance that his universe is now more like the dystopian Frank Miller Dark Knight story. So, they could adapt the Lara Kent (daughter of Superman and Wonder Woman) from that story.
Or, maybe she's a "Clara Kent" female version of Clark Kent in her universe. So Clark/Superman doesn't exist as a male in that universe but as a female instead.
There are lots of possibilities they can go with using the multiverse concept. So, I'm going to withhold final judgment until I see the actress in costume playing the part.
Still, in general, I would prefer these characters to look like how they have consistently looked based on the source material. The actor/actress cast for the part should change to look like the character they are playing (hair dye is the simple solution here), not the character changing to look like the actor/actress.
And I'd feel the exact same way if Supergirl has always been portrayed as having dark hair like her cousin, but now they are making her blonde or a readhead. So, the specific hair color isn't the problem here. It's consistency of the character's look and accuracy to the source material.