Even if Leia had to be found for all the reasons you mentioned -- which are very good ones -- Han didn't have to go himself. As the mission commander, he should have assigned the task to somebody else, IMHO, someone who wouldn't be so desperately missed the next day as they charged against the shield generator.

In a way, this sort of reminds me of Captain Kirk, who always insisted on being the one beaming down to dangerous planets to get into fist fights with the villain of the week, usually also taking his second-in-command with him and leaving poor Enterprise to be captained by whoever they had left behind. Some guys are just too heroic to be put in charge.