The Kirk who let out of his cell a proven murderer/terrorist and then let him near highly sensitive equipment?
That doesn't really scream 'competent'. Quite the contrary.
Kirk sees aligning with Khan as the best way to save his crew, he knows he's going to be played at some point, but he also knows it's that or death for his crew and a war for the Federation because of Marcus. He gambles and it works out in the end because he also trusted in Spock, who tricks Khan. Wise moves all around.
"that or death for his crew and a war for the Federation"?
This very thread presented several easy to find alternatives to these 2 options you falsely present as the only ones available (alternatives which don't involve war or all but allowing a terrorist to continue his rampage).