A point you completely missed.
Gunn's Superman is in its own universe, no connected to any other adaptation, so it is desperate to use music specifically composed for another production. As noted earlier, Bob Harris & Paul Francis Webster's theme to the 1967-70 Spider-Man animated series is undoubtedly one of the most memorable, character-associated themes ever composed, yet it was not shamelessly used as the main title / character theme for Raimi or Webb's Spider-Man films. Neal Hefti's "Batman Theme" composed for the main and end credits of the 1966-68 TV series is another piece of music that was just as known (globally), popular & identified with the character, but again, Elfman (through Burton) was not going to use any of the Hefti (or Nelson Riddle) music for the 1989 Batman movie, since (once again) the movies did not feel one production's music was the default for all other, unrelated adaptations, as each is supposed to be its own creation with its own identity.
Raimi's Spider-Man and Burton's Batman, despite each using existing IPs, were--by rational necessity--creating their own, lone superhero story / universe, not trying to draw the aura and identity from interpretations of others and their unrelated work. Audiences understood and accepted that for both productions.