The point is, and like I already said, Superman is a walking deus ex machina to begin with. Complaining about one of his ridiculous powers and not the others is silly to me.
You misunderstand the nature of "deus ex machina". Superman, like Heracles or Perseus or Gilgamesh or many mythic heroes is beyond mortal Man- true Supes is an extreme example because he's so powerful. Having super powers is not an example of deus ex machina.
In ancient Greek theater the convention of an unsolvable problem by the appearance of a god ( lowered or raised onto the stage by a crane so literally god in the machine). The expression has widened to include contrived solutions to unsolvable problems in stories.
In a pure sense Superman turning back time isn't a true deus ex machina ( because he solves the problem himself) but it feels incredibly contrived and goes against the idea that even he has limits - and yes, heroes rising above their limits is another convention ( Snyder actually does this well in Man of Steel , a more recent example was at the finale of Captain Marvelor Wonder Woman) but it's rarely done in ways as ridiculous as this.
A better way of resolving problems is by a clever use of a hero's abilities ( in Shazam he shares his powers with his family, in Dr Strange he uses the time stone to trap Dormammu).
Another way is via guile - Superman cannot overcome Zod and co in Superman 2, so he tricks them.
None of these are deus ex machina - and when the writers/directors take care to set up the idea by planting hints earlier in the story, these make sense to us as an audience.
What makes the time turning sequence so irritating is the way it's done: whether it is literally what is shown I.e. Superman flying backwards and changing the rotation of the Earth ( which would have wiped out most life on the planet) or him travelling backward in time OR the inference you have drawn which is that he himself flew fast enough to travel back in time.
Neither of these explanations addresses that regardless of how Superman returned to the moment before the catastrophe occurred, he never stops the root cause ( the missiles) if those events . Had he travelled back and helped his past self stop the missiles then that ( while impossible) would have made a bit more sense.
Back to Superman as deus ex machina- yes he's extremely powerful, but not without limits , which is what Johnathan's death establishes - all of that is wiped away by turning back time. It is a contrived solution that undermines the rest of the film.
He didn't resurrect Lois. He prevented her death. My only problem with this is that there were no consequences for Superman's decision.
Well I suppose that's a semantic argument about the nature of resurrection - but I suggest to you that preventing someone's death by travelling back in time, and actually undoing events which have occurred, is about as miraculous as laying on hands or saying magic words or whatever.
Again, this is silly to me. Shooting lasers from your eyes and having frost breath doesn't require you not to think at all? Ok.
It requires you to suspend disbelief- which is what skillful storytellers do. At the Star of Star Wars the first thing we see is two giant spaceships, so we accept that the story takes place in an alien setting ( along with the words " A long time ago, in a Galaxy far far away"). In Superman we hear before the destruction of Krypton that on Earth Kal El will be a godlike being. When we see him doing impossible things we accept it, we suspend disbelief.
Christopher Nolan is very skillful at creating a suspension of disbelief - particularly in the TDK trilogy because he sneaks in impossible things, dressed up enough to make them seem possible, so we accept them. Batman catching a falling Joker with a grapple hook and then hauling him back up is completley impossible - but because so much of the film seems believable, we let it go.
However, the suspension of disbelief is a fragile thing - when a character acts in a way that doesn't make sense, or a jarring or contrived event takes place that suspension can fall apart. The notion of actions having consequences plays a part in this.
You mentioned that Superman turning back time has no consequences, good on you for noticing that, because that's part of what makes that sequence particularly uncomfortable.
In comparison, Dr Strange, uses the time stone to create an endless loop that traps Dormammu, thus saving Earth. But as a consequence he's trapped in that loop too. Now, if he'd been able to use the time stone to trap Dormammu in his own loop, without being trapped himself ....well that might just seem wrong and might cause the suspension of disbelief ( that a glowing green rock can control time) to collapse.
So, as for my suggestions about why the writers fell back on the turning back time option, well you're right I've got no basis for that.
That is different from your statement that the reason Superman doesn't use his newfound time travel powers to then save his father's life " because the story didn't need him to" . That is like saying it didn't happen because it didn't happen, a non argument.
Ultimately we aren't going to agree on this, but there you go. Fortunately the thread is big enough for both our points of view.