I'd like to see an Elseworlds story where Superman arrived on Earth as an adult and never adopted a secret identity. It'd be interested to see how different he'd be.
Hmmm! Sounds like a fun bit of speculation; let me give it a shot.
Krypton was defined as being a race of beings that were morally upstanding, "possessing a greater capacity for good," in the movie's own words. In the first appearance of Nightwing, when Kandor was re-enlarged on Earth and the Kandorians had superpowers, it didn't go to their heads: "NO! This world belongs to the EARTH RACES!"
And nobody has mentioned yet, but it is interesting to note that on a planet the size of Krypton with a population equivalent surely, to the developed world, there are only a few dozen or so violent criminals worthy of being placed in the Phantom Zone (compare with our own society's problem of prison overcrowding).
So, in that light, it is entirely likely that if Superman came to earth as an adult after being rocketed from Krypton, he would still become a superhero, especially being a son of Jor-El as he is.
But here's some possible points of divergence:
Lois has no competition from Lana, because Lana never knew Superboy in Smallville.
Superman would wear standard Kryptonian clothes (headband, possibly a Jor-El esque sun suit) as there is no Martha Kent to weave him a costume (though his Krypton clothes to earth eyes would be exotic to the point of being a "costume").
As there is no Clark Kent, Superman would never know Jimmy Olsen, however, it is likely the spunky, driven Lois would pursue him just the same, and so he would still make her acquaintance and capture her imagination.
Superman would regularly leave earth much more frequently and for far longer periods to explore space, becoming much more like Mon-El from the Legion; after all, there is nothing keeping him on earth specifically.
And speaking of the Legion, as Superman is far too old to be made into a member, he would never have joined that organization.
Mon-El would have briefly stopped on Earth, and left for space once he recovers his memory, and never have been trapped in the Phantom Zone or become a Legionnaire, living a long, full life when he returns to Daxam.
Luthor's rage was directed against society, not against Superman in particular, and so even without Superboy he would have become a villain. Their relationship however, would be much cooler instead of the rage that Luthor directs at Superman.
The Superman/Batman Team may not have happened the way it did. Actually, what might have happened is that Superman, being an adult with memories of a family on a distant planet, would become allies with another Justice Leaguer with a similar story he can empathise with: the Martian Manhunter, and the Superman/Martian Manhunter Team would replace the Superman/Batman Team.
Superman, growing up on a technological society like Krypton and the son of a scientist, would be a more technical hero; probably using all manner of tiny supertechnology to advance his personal existence.
Superman would not look down on human beings, however, he would have a type of planetary chauvanism that would only manifest unconsciously; he's too nice a guy to be arrogant or aloof. Rather, it would be sort of like Lightray in NEW GODS: "I should be able to modify the device to transmit on your primitive 'television' system...oh, I apologize. Your Earth civilization's achievements are many and great."
Superman would spend more time in the Fortress. Growing up on Krypton, he would be sentimental for that planet all the time.
Martha and Jonathan Kent would still be alive without Superboy to deliver to them that deadly virus.