Hmm, I see what you're saying; certainly the 1940s Superman radio series did some impressive storylines in its post-WWII years about fighting racists, Neo-Nazis and other aspiring fascists, and anti-immigrant demagogues. But on the other hand, the disadvantage of something like that is that actors of color in the cast (since the modern practice is usually to match the ethnicities of animated character and voice actor) would be relegated to playing a limited range of character types and professions and would only be able to participate in the stories in limited ways. Only the white cast members would really be free to play a role in stories that weren't about racial injustice, or to play characters other than servants, laborers, singers, dancers, etc. It seems fairer to the actors to create a show that allows them all to participate equally in a wide range of stories.
In a realistic 1940s setting, the character most likely to be black would be Alfred, and that could be kind of uncomfortable. Certainly a 1940s Bruce Wayne would probably have treated a black Alfred well, as well as Jack Benny treated Rochester (the one black character in 1940s radio who was written respectfully and never put down with racial stereotypes, because Benny insisted), but to modern eyes it would still be a stereotyped and servile role and thus problematical. (Though on the other hand, a story about a forbidden romance between Batman and a black Catwoman might be interesting.)
Presumably the reason Timm embraced the '40s setting was nostalgia for its style, the tone of its comics and movies, its fashions and music, etc. If nostalgia for an era is the driver, I can see the appeal of creating an alternate fantasy version that has the good things about that era without the bad. Yeah, it's dishonest about the reality, but it's more of an aspirational fantasy. A show that confronted the darker realities could be worthwhile, certainly, but it might be too depressing, especially with the foreknowledge that things would not get much better for the characters of color in their lifetimes.