I like the concept of Superman living in real time. It was one of my favorite things about the Bronze Age Earth-2. It was interesting to have a Superman who was supposedly the result of 30-50 years of history and seeing things like Mr & Mrs Superman or Roy Thomas' All-Star Squadron made it even better.
But as even a separate on-going today I cringe at the thought. DC doesn't really have the type of writers needed to handle this. Sure you might find a Morrison who could keep the fictional continuity straight or a James Robinson who'd put in the effort to make a story feel like it was occurring in 1938, 1952. or 1967. But do you think they would stay long enough? Do you think DC would try to find someone else of equal talent when they left?
And even if we didn't get a lot of new stuff set in the early days, we'd still have problems fitting in the Weisiner era of "reuse the same story every few years" with any type of continuity that isn't a parody. For all of his use of classic Superman tropes in Supreme, Moore didn't bring up Supreme encountering "Supreme Jr" one year and "The Second Supreme" a few years later and "Supreme's Long Lost Brother" a bit after that. Or are we cherrypicking what issues count out of Superman's 75 years so we don't have Mon-El, Hal Kar, Hyperman, Super-Menace, Johnny Kirk, Skyboy, ... all trying to fit in the same history.