Well....that's not entirely accurate.
If you look at the dates, Green Lantern went out of publication with the May 1949 issue (GL having already surrendered the lead spot in his own book to Streak, the Wonder Dog!

), the Flash packed in it in that same February (the "All-Flash" sister book having vanished in 1946), More Fun switched from heroes to gag strips in 1945, All-American transitioned to western strips in 1948, and so on. Adventure managed to soldier on by becoming a de facto Superman Family title with Superboy in the lead, and the various second-tier heroes, having lost their own books, huddled together as the JSA until 1951 when All-Star Comics became All-Star Western.
And that's just DC. Timely, having put all its eggs in the Axis-busting basket, essentially imploded when the war ended, with Captain America limping along as a crime/horror book until 1950, Sub-Mariner sunk in 1949 and The Human Torch burned out that same year (sparking to life for 3 more issues in 1954).
Dr. Wertham's book, "Seduction of the Innocent" and the resulting Senate hearings under Estes Kefauver didn't come along until 1954, so it's safe to say they were NOT the reason the Golden Age of Superheroes ended. When they showed up, it was already over. Indeed, the whole anti-Comics hysteria came about because comics in the 50s had moved to horror and "True Crime" content in a desperate effort to reinvent themselves after the superhero craze fizzled out.
So what did end the Golden Age? Reader apathy, mostly. Books about cowboys, cops, funny animals, goofy teenagers and love-challenged heroines sold better than books about people in longjohns punching each other in the face. The industry adapted. Also television came along, and not too long after that paperback novels and other entertainments that ate into the comics audience.
The only characters to survive were DC's "Big Three," who had already become icons bigger than than their source material (and much more adaptable than, say, AirBoy or Hangman) and Fawcett's Marvel Family, which was never your stereotypical "superhero" fare anyway...it owed as much to Archie as Superman.
As for how the other DC heroes would have adapted had they survived, I think we saw the beginnings of that before they vanished. They tried to add humor, or animal sidekicks, or whatever it took. It didn't work, whereas the same gimmicks for Superman and Batman did work. Then when the late 50s and 60s rolled around and the focus turned to science and technology, we got those characters reinvented in new forms. I'm not at all sure they could have adapted nearly as well as they were "rebooted" (Alan Scott as Hal Jordan, Jay Garrick as Barry Allen, etc).
The really amazing part to me, looking back, is that there were only seven years between Jay's last appearance in All-Star #57 and Barry's debut in Showcase #4. So really only seven short years separate the Golden and Silver Ages, depending on how you look at it. Seven years is nothing today. Heck I think there are cross-over events that last that long.