As for Kal-L, maybe I'm wrong but I never thought they said he gave up his secret ID. I could have sworn I saw some 70's All Star comics JSA stories which had Clark changing into Superman.
Kal kept up the Clark Kent disguise right up until his final appearance in Crisis #12.
What I was referring to is the period AFTER that. I gather from what I've seen of IC that Kal-L has been in his Super-suit since his "goodbye" in 1986. Everything I've seen suggests he wore the cape and tights full-time in that "paradise" dimension, watching events unfold on Earth-Dreck.
Personally, I would've thought that in "paradise," Kal would hang out in flannels and jeans. Or maybe a Kryptonian tunic or something. Anyway it seems odd to just lounge around in paradise for two decades wearing your battle gear. If everything's so perfect, why do you need super-heroes at all?