Handing over the password only gains them the additional access to private messages, over what is seen with full access and no password. Offering password access violates the confidence of your friends.
I don't have a FB account, but If I did and were asked for the password, I offer to give it to them but ask to first swap paper that acknowledged that they were asking for access to information contained in private messages about my age, marital status and religious views..
There are some jobs that where the public image of the person is the essence of their employment. For example, a minister in view of a call should not balk at granting full external access, but not the password. There could be private messages that would be protected by pastoral priviledge or even by HIPPA laws.
The employers that require FB passwords will eventually be paying a premium in salaries for the right to access, as it should limit the pool from which they are able to draw.