It wouldn't seem weird if it had happened that way, and I suspect under this scenario under which Johnny Quick and Doll Man are continued uninterrupted instead of a new Flash and Atom, we'd likely never have had an Earth -1 and 2.
I've actually seen tiny hints as to what a Justice League might have looked like under similar conditions. I mean, given that several titles were already being published, might Julie Schwartz have decided to revamp some of the marginal characters anyway? And how often in Silver Age DC does the name "Jack B. Quick" show up, anyway...?
A long while back, I entertained myself by considering what might have happened if All-American Comics had died off, leaving the DC-side to continue All-Star alone without the other characters. It was an interesting exercise to see who was available at different times, who might have had the market potential, and the likely effects on what we'd now call continuity.
Like, does Elastic Lad get farmed out to be Flash's glory-hound pal? Since Robotman is a likely nod for the League, does the Martian Manhunter get shunted to the Doom Patrol? If he does, what does that say about Mento or Beast Boy, who each have some obvious similarities to the multi-identitied Martian?
What about some names for the new teams? Here are a couple of ideas:
Fox heroes - Foxforce (might be cued by the military alphabet Alpha, Bravo, etc., Fox being for F)
Ace heroes - The Avenging Aces
Lev Gleason - Freedom's Furies
Prize heroes - The Prize Patrol
Several Prize heroes did come together as the Crime Crushers to fight the not-Frankenstein-because-that's-the-doctor-but-we're-calling-him-that-anyway. And Fawcett had both the Crime Crusaders Club (a real, though small, team) and the Squadron of Justice (populated by Marvel Family members). And the Harvey group has already been mentioned, referred to as "America's Stars" or somesuch.
Gleason had the makings of a team, though unnamed, by teaming everybody (including the Claw) with Daredevil against Hitler. The Novelty characters were likewise banded together at the request of Uncle Sam, though they didn't cross over.