It's not just that they have had a hate on for all the Golden Age characters including the JSA -- it's that they seem to hate Alan in particular. Maybe it's because he was the original Green Lantern and they can't forgive him for placing Hal Jordan in a permanent Number Two position.
It wasn't so obvious in the JLA/JSA crossovers, because there were so many characters and they were usually in competition, not with each other, but with assorted super-villains. But whenever Alan and Hal went head to head in Hal's own book, Alan was usually made out to be a poor second-best, requiring Hal to bail him out. (The only exception was #45, "Prince Peril's Power Play", where they started out with separate storylines and weren't aware they were rivals for Princess Ramia's hand - and she chose neither of them, preferring Alan's comic sidekick Doiby Dickles, because he loved her so much and he was so amusing. But even so, the misleading cover shows Alan at Prince Peril's mercy and Hal zooming to the rescue.)
The beatdowns continued through the All-Star continuations (1976-1978) and into the Infinity Inc. era, during which Alan lost control of his broadcasting company and had to start over from scratch, working in Keystone City under Jay Garrick (the Golden Age Flash - it's interesting that Jay never gets the same sort of beatdowns and disrespect).
Partway through Infinity Inc., Crisis on Infinite Earths hit, reducing the former Multiverse to just one Earth. Alan made out better than some, as he could be retrofitted into the unified timeline without any major problems (don't ask about the Hawks, and especially don't ask about Wonder Woman...). But that just intensified the conflict vs. Hal Jordan, until the JSA were whisked off to "permanent" imprisonment in a pocket universe where they remained constantly fighting and re-fighting the battle of Ragnarok.
Another terrible injustice was dealt the character about this time: the Green Lantern "Special 50th Anniversary" issue, which Alan was hardly even in because he was stuck in Ragnarok - even though this was his 50th anniversary, not Hal Jordan's.
About this time it was explained in "Sandman: Season of Mists" that the JSA's pocket universe was contained in a crystal ball created by the Norse God Odin, which he was using to study ways of avoiding Ragnarok. This gave DC an idea to return the JSA to continuity, which they proceeded to do in "Armageddon: Inferno". But their next real-time appearance, as a team of aged but indomitable superheroes ("Justice Society of America", 10 issues, 1992) sealed their doom. The magazine was summarily canceled before the first issue was on the stands, and the JSA was marked for destruction in the upcoming event, "Zero Hour".
Alan survived the event (half of his teammates did not), but stripped of his power, or so he thought, and forced into retirement - which at least meant he could spend more time with his family: daughter Jade, son Obsidian, and second wife Molly "Harlequin" Maynne. (What was going on behind the scenes was that DC had decided to get rid of ALL its Green Lanterns and start over with just one, a nebbish Everyman named Kyle Rayner. Hal became an omnicidal maniac, John was crippled, Guy Gardner became a barbarian warrior, and the rest just...died.)
DC eventually relented enough to allow Alan to regain his power, but for years afterward he had to go under the absurd monicker of "Sentinel" for reasons never explained. This meant that he was available to join the reconstituted JSA along with fellow survivors Jay (Flash) Ted Grant (Wildcat) and, eventually, a disambiguated Carter Hall Hawkman. But since he was so much more powerful than the rest of the team, he was frequently Worfed so that they could step forward and show their stuff. (It was after one such Worfing that he finally regained his proper title.)
Probably the nastiest thing DC ever did to Alan occurred during the later phase of this era: the Elseworlds, "Green Lantern: Evil's Might". What they did, and never admitted to doing, was to Evil up Guy Gardner and hang Alan's name on him. Why they did it, I have no idea - but whoever came up with that excrescence should spend the rest of his (or her) life on the breadline.
By this time DC was stumbling and bumbling from Crisis to Crisis to Crisis, making coherent storytelling nearly impossible. The JSA ongoing was canceled, restarted, restarted again, and Alan got Worfed for the last time in that continuity, worse than ever (broken neck, confined to a metal exoskeleton, finally perishing in green flame, or so we were told).
Then poof, the New 52 happened, and there never was a 1940s JSA, never was an Alan Scott Green Lantern, none of those stories - or any older stories - had ever happened, and everything was All-New, All-Now, All For The First Time. DC teased a "new ongoing" JSA book, and gave us -- "Earth-2", where some people had the same names but everything was different and it was All-New All-Now. Well, that stumbled from Crisis to Crisis to Crisis and was finally mercy-killed, with a "JSA" of sorts finally cohering only in the last pages of the last issue.
DC is still stumbling, bumbling, and fumbling from Crisis to Crisis to Crisis, but some of the history has begun to creep back in. So far the signals are very, very mixed and we are being whacked over the head with "This Is Not Your Grampaw's JSA" - if, that is, they are ever allowed to return as a superhero team.