He's cheated death and escaped the clutches of the Chinese and the Russians.
He's evaded the US intelligence agencies.
So we know if there's money for another season, Jack will be out.
So why bother even having the scene of him surrendering himself (and of course the predicate of having Chloe get captured)?
Maybe they wanted to end the seasons on a somber note. Rather than triumphalism for Jack saving the world again and again, they have to emphasize the personal sacrifices he's always making, being alienated from his daughter and grandchild, not being appreciated or treated like the hero by the people whom he's saved, etc.
They did that in past seasons, him walking off alone into exile, not receiving any expressions of gratitude.
Yet we know he doesn't hold a grudge because he always comes back when there's a plot brewing. He doesn't mind going off alone at the end of seasons but he's somewhere, always monitoring situations to come to the rescue again. So he's like an unmasked Batman, taking vigilante action to the nth degree. Batman only helped the hapless Gotham PD but Jack is doing the job that the intelligence community of the lone superpower can't do.
It's like a co-dependence situation. He can't stay away from the action, when there's a plot, he has to show up. Now, he's not some glory or famewhore, maybe just addicted to the action, to killing, torturing, screaming, etc.