No, they wouldn’t. There are currently only two non-Monitors alive who recall the previous Multiverse - Power Girl and Superman-Prime. Because they are the only ones who existed in it.
The universe was rewritten twice before being rewritten as a multiverse again - immediately after Crisis, when Psycho Pirate was the only one who remembered, despite the anomaly of Power Girl (which resulted in her history being revised repeatedly), and in Zero Hour, which smoothed out some anomalies, and worsened others.
Superman, Batman, Wonder Woman, Batman - everyone, in fact, save the two above - is a completely new person.
Thanks to the existence of Power Girl and Prime (and the late Superman-2 and Alexander Luthor jr), they know that there was a multiverse, but they know little about it, and all of that is filtered through Peeg’s knowledge, and Prime’s psychosis.
The JSA currently has no room for doubt that there is a multiverse now - Superman-22 is currently staying with them.
Some quibbles with the OP:
We haven’t seen the Earth-1 Superman, yet - Earth-1 and New Earth are explicitly different universes, the latter invariably referred to as such.
Monarch is the New Earth Captain Atom - we have only gotten a single panel glimpse of Earth-4 or any of its characters, yet, and, save for Blue Beetle (who was shown in the Dan Garret uniform), they resemble the Charlton versions closely (on the other hand, their look should be taken with a grain of salt, as Earth-10’s Justice League analogues had their uniforms changed (for the worse, IMO)).
Also, Captain Atom is an archetype unto himself, not a Superman analogue.
Clark Kent never appeared in Planetary - only the Terra Obscura Elseworld, which is not Earth-50. The actual Earth-50 Superman analogue would be Majestic, The High, or Apollo. Or one of the half dozen versions Ellis murdered in Planetary proper, Stormwatch, and the Authority.
Re: Earth-15 - Zod and the Justice League created a utopia where they’re hardly needed - you’re going to call them incompetent because the most powerful (arguably) mortal being in the multiverse murdered them?
Supermen 2 and 22 are the very definition of ‘heroic’ to my mind - while they both screwed up (and big), they eventually realized it, and stood up to fix it. 2 died in the process, and 22’s attempt, while ultimately successful didn’t come without a price, but being right every time isn’t a quality necessary for heroes - but standing up to fix things - even - ESPECIALLY - if it was your mistake that screwed things up in the first place - is.
By the standard set up in these entries, nobody, on any Earth is even vaguely competent. (New Earth’s Batman especially, since you mentioned him.)
If you’re going to count Hank Henshaw as an ‘evil Superman’, then he’s balanced by Steel or Superboy (the other being balanced by the Eradicator).
Earth-9 - That title doesn’t actually sound particularly sinister. In fact, given that the only new Tangent material mentioned in anything I’ve seen from DC (or, doing a Google search, anywhere) is Global Decree, which deals with the death of their Superman, reference to ‘Superman’s reign’ seems a pretty blatant reference to the Reign of the Supermen.
Earths 3, 10, and Anti-Matter, Almost everybody who’s good on New Earth is evil - from Superman on down to Commissioner Gordon.