Because Superman, Batman, and Wonder Woman continued publication after the JSA's solo titles ended in 1949 with the team's adventures ending in 1952 though some diehards like Aquaman and Green Arrow held on. Once they had a changeover in audience, Julius Schwartz had the big-brained idea to bring back new versions of Flash, Green Lantern, Hawkman, and Atom with a sci-fi flavor. Then Gardner Fox wrote the "Flash of Two Worlds" in 1961, which birthed the multiverse the DC imploded twenty-five years later with Crisis on Infinite Earths. DC was exploring the generational heroes concept with Infinity Inc. pre-Crisis, but that was Earth-Two whereas Earth-One was designed to be the "modern" universe with the floating timeline.
Crisis ultimately created more problems than it solved despite the best of intentions. Instead of streamlining the DC universe, it created a knotted timeline that generations of writers have made worse to this day. In the case of Superman being the first superhero, merging the five remaining Earths (One/Two/Four/S/X) basically put the kibosh on that. Frankly, I don't the the need for Superman to be the "first" superhero; he needs to be the greatest, and whose deeds inspired others well into the Legion of Super-Heroes' time and beyond. (e.g. Justice Legion Alpha to the 853rd century.)
Future State: Flash is one of the most mean-spirited stories ever written because of Dan DiDio's spiteful hatred of legacy heroes (hence why the Teen Titans got the cannon fodder treatment) and I believe that his fingerprints are all over this despite his firing. Full disclosure: I lean towards Barry because I'm a Silve/Bronze Age nerd, but I grew up with Wally and loathe this story with every ounce of my being. Say what you want about Geoff Johns: he wrote a damn fine Wally run from 1999-2005 and I genuinely believe that he liked and respected the character. Hell, I don't think he would've placed Wally front and center during Rebirth if he hated the character. Similarly, Josh Williamson treated the character with due respect and even tried to "redeem" the character during the end of his run.
Barry, Wally, Jay--fuck I don't care which Flash takes center stage. As long as the story is engaging, I'll read it. Same thing with the dozen or so Earth-born Green Lanterns DC has flying around.