Ah, but that was before he got himself into shape! Otherwise, he would have retired early, and never have helped found the JSA when he finally became "lean, muscular, and heroic" which is why he kept going, stayed on the team, and switched to the new costume and took on the young sidekick.
That's probably the reason Wildcat was never an active JSA member until recent years. He was too busy training other more active heroes like Al Pratt and Wes Dodds, getting them into much better shape in order to survive "mystery men" action without the benefit of full super powers.