I can see your point that the usual mode of operation of actual Satan is not to save the person’s spirit. Turning the man over to Satan here, then, in 1 Corinthians 5:5, could be a metaphor for allowing the man to be immersed in and consumed by self-generated depravity, some of which was on display while the man was a member of the Corinthian church.
Paul uses the same type of language in 1 Timothy 1:20.
“Among these are Hymenaeus and Alexander, whom I have handed over to Satan, so that they will be taught not to blaspheme.”
In the 1 Corinthians 5:5 passage,
“I have decided to deliver such a one to Satan for the destruction of his flesh, so that his spirit may be saved in the day of the Lord Jesus,”
Paul arranged this consuming immersion in depravity by instructing the church to sever all ties with this man and thus to let him live without that strong, potentially positive, but to that time, ineffective force in his life. (Note that this instruction–apparently–occurs in the last part of 1 Corinthians 5:13, “. . . REMOVE THE WICKED MAN FROM AMONG YOURSELVES." This instruction to the church to remove the man would make little sense if the man were to be killed as part of Paul’s turning him over to Satan.) After the man was removed from the church, he lived totally with his depravity–with no counter from the church–until he realized the truth of his situation. That was the start of his repentance and led him to the sorrowful state that Paul refers to later (if he indeed does). The man’s welcome back to the church (if this man is indeed the one referred to later) furthered his continued repentance until he was free from this depravity, a depravity that was eventually recognized by the man only after he was immersed totally in it, i.e., only after he was turned over to Satan.