Self-sufficient and independent may be admirable, but it's not as interesting.
Superman is near perfect physically. Is he meant to be near-perfect mentally too? Rarely has doubt, or fear, or anxiety, or is unsure of himself?
Personally I'd prefer to see a Superman on screen who, whilst he's pretty self-assured most of the time, does
have to struggle with certain things when he's put in complex situations. And I don't mean silly things like should he save someone's cat up the tree, or leave it there to teach them to look after it better
I'm talking about massive Earth-changing decisions like should he help out in areas of famine or war? Or should he let humankind stand on it's own 2 feet and learn from their mistakes? Should he give humans access to Kryptonian tech to better themselves, or allow mankind to progress naturally? These are the kind of things he has to grapple with when he has the power to change the world at his disposal, never mind the other unique situations he may find himself in on any given day.
And in those situations ....................... he does what most humans would if they're blessed enough to be able to do so : talk to their older, wiser parents and get some perspective & advice.
It doesn't make him weaker because he's 'running home to mom and dad'. If anything, with the massive power he has available to him and the fact that he can pretty much do what he wants without being easily stopped, it's admirable that he still seeks the counsel of those 2 humans who taught him to cherish life and treat people with respect.