Obviously, what got me thinking about this is the Dark Multiverse COIE one-shot (which is really Dark Multiverse: Last Days of the JSA, but I guess they expected COIE to sell better, not unreasonably), but I don't really buy the premise of that, which was that the entire Justice League found themselves on an Earth-2-based Post-Crisis Earth with no history, like Kal-L, Huntress and E-2 Robin in Crisis #11. If you flip the situation, you get the E1 duplicate characters - E1-Superman/Kal-El and Supergirl/Kara Zor-El, E1-Batman & Robin, E1-Wonder Woman, E1-Green Arrow and some consequential & supporting characters wiped from history. But not the rest. (After all, DC would still have titles to publish!)
Just thinking, as a counterfactual... if they committed to keeping the older versions around, what would have changed?
Funnily enough, several of the changes which would have happened were done *anyway* - Superman, Batman & Wonder Woman were all removed from JLA history for different reasons (eventually codified years later as JLA: Year One, telling a version of the JLA founding without the "trinity" and with Black Canary Jr as a founder) - the only significant difference would have been losing Green Arrow too. (E1 Aquaman was different enough to be more like E1 vs E2 Hawkman, with both co-existing despite similar names. Maybe without Aquaworld bringing it all crashing down a few years later). Meanwhile, the Legion lost Supergirl and got a "pocket universe" E1-Superboy.
The biggest change outside of the "trinity" books would probably be the Titans losing Dick Grayson/Robin/Nightwing, which would have caused major problems for that book (also Speedy, but since he wasn't an active member it would have been less disruptive. Funnily enough, Donna Troy would not have been messed up in this scenario, she just gets saved by an older WW...). How they patch that... the most obvious thing would be to have Jason Todd (who was basically a Young Dick expy pre-Crisis anyway) backdated, I suppose.
Since Superman & Wonder Woman were an alien and from a race of immortal Amazons respectively, they could have been active in the present day without too much trouble, and Superman in particular was a "father figure" of sorts anyway. They might have gone less heavy on the aging effects than the E2 versions were shown with in Crisis, but they would still have been viable. Supporting characters, especially for Superman, might have been more of a problem though.
Batman, well, in this scenario we're keeping the basic history of the Earth-2 versions, so he'd be dead. I'm guessing that Batman as a franchise would have got a variation of the treatment Wonder Woman got in reality - we introduce a new Batman in the present day. They just wouldn't be Bruce Wayne, but "inspired by" him, probably with Frank Miller getting even freer reign to design a "Next Batman Year One" than he did for the actual Batman Year One. Some past stories that really needed an unavailable Batman would probably get plugged with Huntress, with Jason Todd in place of Dick (as in the Titans idea above).
Most of the rest ends up similar to what happened in reality - so Wally takes over as Flash, Justice League Detroit putters on for a couple of years, etc - but with fewer outright reboots (so Captain Marvel/Shazam continues from the 70s version rather than getting rebooted twice in a few years), and a greater JSA presence with no "Last Days..."
I'm not sure it would have been "better" than what actually happened, and it would certainly have required a very different line of editorial thought, but I found it an interesting line of thought to run down, at least.