Keeping his power in check hasn't been *that* much of a struggle for him most of the time. As he grew up and learned of his powers, he's had to develop massive self control after all. And as Clark Kent, in MANT adaptations, he manages to be clumsy and uncoordinated a good amount of the time, yet doesnt destroy the city or anything. Sure it can come up in battles where he has to put in work to defeat his greatest foes, but even then there are great adaptations like the animated series where he still struggled against foes WHILE having to hold back.

That's another thing actually, him holding back leads to villains getting opportunities to blindside him or get a lucky hit off that he wasn't expecting! I'd bet that's what's behind all the scenes in the trailer of him struggling: he can't just unleash himself fully to deal with villains, but in doing so he has to put in more effort and deal with more attacks and such against him that otherwise, had he no reason to hold back, he could do away with easily.

He's "human" as in he understands very deeply what it is to be a normal person. That's how he lived for most of his adolescence. That's why he's a hero now instead of a selfish villain or an awkward visitor who doesn't understand the Earth and tries to "fix" it or something. It's that humanity in him that contrasts so well with people like Lex Luthor, who are more callous and disrespectful of others' lives and ambitions and hopes and crap. Superman at the end of the day is a better person than a lot of real humans, and thusly still can serve as inspiration or a symbol of hope despite his immense power.

Also, plenty of Superman's most popular adaptations were on the weaker side. Take shows like Smallville or Superman: The Animated Series for instance; he wasn't nearly as powerful as the comics version who pulled a solar system on a chain or shot himself from his fingertips in either, and yet those stories were still well executed. Or in the animated show's case, so popular and iconic as to be one of the defacto versions for a whole generation.