The special edition of Superman: The Movie included a scene deleted from the theatrical cut, where Jor-El explained to his son that it was important to maintain his secret identity so that he wouldn't be expected to serve humanity 24 hours a day, and to prevent his friends and loved ones from being targeted by his enemies.
JOR-EL: You are revealed to the world. Very well, so be it. But you still must keep your secret identity.
JOR-EL: The reasons are two: first, you cannot serve humanity twenty-eight hours a day.
JOR-EL: Or twenty-four, as it is in Earth time. Your help would be called for endlessly, even for those tasks which human beings could solve themselves. It is their habit to abuse their resources in such a way.
SUPERMAN: And, secondly?
JOR-EL: Second, your enemies would discover their only way to hurt you: by hurting the people you care for.
SUPERMAN: Thank you, Father.
Superman: The Movie - Special Edition (1978)
These sentiments are somewhat echoed in various Superman comics, such as those cited below.
SUPERMAN: Obviously I can't be "on call" twenty-four hours a day. Even I need time to relax and unwind. To be human for a little while. That's why it's lucky I didn't get the chance to tell anyone my name after I saved the shuttle. Now, with a few minor alterations, I can have a private place where no one will ever think to look for me -- a "Fortress of Solitude," so to speak. Meet the new Clark Kent!
JONATHAN KENT: See, Ma? With his hair all slickered back and an old pair of my spectacles, his whole face seems to change. All he needs to do is stoop a tad, and he looks like a whole different man. And so long as he's careful never to let on that he has two separate identities, he'll be able to move freely, like ordinary folks!
The Man of Steel #1 (October, 1986)
SUPERMAN: It all started in Smallville. Right in this room, I thought about giving up Clark Kent completely. But I like being Clark Kent. I like who I am and who my parents were. So I came up with the idea of a dual identity. I thought about wearing a mask like Bruce does. But as close as we are, Batman's going for something different than I am. I'd rather good people trust me than bad people fear me. I think they need to see your eyes for that. So Clark Kent wears a mask instead of Superman.
Justice League Vol. 2 #15 (February, 2013)
JON KENT: Dad, I got another question. Is it hard being Superman?
SUPERMAN: How do you mean?
JON KENT: Well, you don't get paid. An' there's so much wrong in the world that you could be doin' this 24/7.
SUPERMAN: Heh. True enough. But I work at trying to find the right balance of doing what I can while also having a personal life. You and your mom need me to do that... and I need it too. I'm still Clark -- a husband and father -- every bit as much as I'm Superman.
Action Comics Vol. 1 #967 (January, 2017)
Superman wanting to spend some time living a somewhat normal life -- as a break from his role as a superhero -- makes sense to me. Despite his alien origins, he appears to feel most or all of the same emotions that humans do, and values his relationships with his friends and loved ones as much as a normal human. His having human-like emotions is especially evident when he's portrayed by human actors, but it's evident in the comics as well.
And sure, he's more self-sacrificing than most, but is he completely devoid of selfish desires? Apparently not, or else he surely wouldn't waste time pursuing romantic relationships, as he does in most continuities. He'd spend every waking second serving humanity in general... but living solely for others like that would likely take a toll on the mental health of someone who's portrayed as being as human psychologically as Superman is.
So if we accept that Superman is human enough on a psychological level to want (and possibly even need) some downtime, and the opportunity to experience normal human-style relationships, that explains the value of a secret identity, both as a means to be seen in public without constantly having to live up to the expectations of being Superman, and to avoid placing a bullseye on the backs of everyone he's known to have personal relationships with.
Does it guarantee the safety of his friends and loved ones? Clearly not, because his enemies can and do occasionally draw a link between Superman and people he cares about, as seen in Superman II, when Lex Luthor advised General Zod to take Lois hostage as a means to draw Superman out. However, the danger to his friends and loved ones would be greatly magnified if the full extent of his personal relationships were widely known.
Also, I'm not sure how practical it'd be for him to abandon the Clark Kent identity as an adult and openly work at the Daily Planet as Superman. If Superman were known to work at the Daily Planet, that'd surely make everyone employed there and the building itself a target for his enemies. And if it were known that he used to be Clark Kent, that'd make everyone he grew up with in Smallville a target for his enemies as well.
He could try and keep the fact that he used to be Clark Kent a secret, but in order to prevent anyone from drawing a link between Superman and his friends and family in Smallville, he'd either have to entirely end his relationships with those people, or find some other way to maintain those relationships inconspicuously. Why look for some other way to maintain those relationships inconspicuously, when he could already do so as Clark?