I suspect this has more to do with the original historic images of Superman from the early covers of Action Comics and the Fleischer Superman animated films.
YouTube keeps a nice collection of the Fleischer films on hand with decent video quality.
In the early radio programs and even from the very first Fleischer film Superman (aka The Mad Scientist ) Superman was supposedly "leaping" from place to place.
But artistically having to show our hero jumping around was stylistically difficult given the film lengths and effort required to make them.
So his leaps would transition from a jumping movement where he would use his running momentum to jump and his hands to point skyward.
This often transitioned into a swimmer's pose with his hands at his sides as he would begin to "fly" and gain speed.
It was from this position he would streak to his target "like a speeding bullet."
Look at the Mad Scientist from 6:36 to 6:40 showing a jumping to flight transition.
He would often, however, have to deflect materials, bullets, shells, deadly beams of energy and would use his hands to do so.
This lead to a pose where he would have at least one of his hands out in front of him to catch or deflect incoming attacks.
He would also do this if he were carrying someone to protect them as well.
This ultimately lead to the later flying scenes where he would be shown flying and artists treated his flying as if it were a form of anti-gravity swimming where he would alter his direction by twisting his body and changing his leading pointing hand.
Today, I would consider it a matter of artistic style, not necessity as to why he might keep his hands out or at his side while flying since the character is so far removed from his origins, artists are likely to assume such poses for appearance sake, not even remembering how or why they came to be.
scifi.stackexchange.com/users/2765/Thaddeus Howze
In universe: Just looking at his shape in the two illustrations you posted, I'd guess it is to reduce air resistance.
This is similar to why swimmers dive into a pool with their hands extended, so they can slice into the water with less resistance.
Out of universe
: It looks much more heroic to be drawn that way.
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I always suspected it was to steer and maintain his balance.
It would be undignified to be sideways.
scifi.stackexchange.com/users/3576/Adele C
I read a theory that he was using the hand out front to keep a sightline with the horizon.
This is the same as glancing at the corner of the car hood to make sure you're not weaving.
Maybe he just wants to keep his flight level.
Getting pulled over for weaving is bad enough.
Having the Air Force think you're flying drunk would be worse.
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To protect his face He may be indestructible, but there are other indestructible things and beings in the DC universe.
On top of that, invisibility is a thing.
If he's going to crash against Wonder Woman's invisible airplane midflight, it'll hurt less if he hits with his fist than if he hits with his face.
It's pleasant
Ever got your arms out of the window of a moving car?
I feel the windy senstion is really pleasant.
Maybe Kal-El just likes the way the air moves around his arms as he flies.
He's mimicking a swimmer When athletes jump in the water, and in at least one swimming style athletes will keep their arms in front of them like that.
Not only that, the whole body position is similar.
The difference is that Kal El looks head instead of downwards and sometimes he makes fists rather than having his palms open.
Maybe he saw people swimming before and he originally thought flying was like swimming in the air.
That stuck with him and he never had any reasons to change how he flies.
Compare with Marvel's doctor strange, which flies purely by magic, and also Marvel's Thor and the little prince, which fly by holding on to magic tools.
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Aerodynamics of course.
It's like a stealth fighter jet...
It has a long needle on the nose to help break the sound barrier.
Same concept with superman.
But that's just my take on it.
scifi.stackexchange.com/users/19321/Zach
When Superman flies his typical position is either one arm, or both out in front of him (either flat palm or fist closed).   There are occasions where he does fly with his arms at his sides (usually when he's going for maximum velocity).   Obviously he doesn't have to worry about aerodynamics, is there ever an in universe or  "Word of God"  reason given for this pose?
Why does Superman put one or both arms up when he flies?
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<dc><superman>
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This is to do with the original historic images of Superman  and it looks much more heroic to be drawn that way. There is a theory that he was using the hand out front to keep a sightline with the horizon, or maybe he just wants to keep his flight level or he does this for protection. Having his arms raised helps steer and maintain balance and protect his face.
Having his arms raised helps steer and maintain balance. In this way he can protect his face. Aerodynamics do appear to play a part.