Suppose the blackmail is against not the politician, but someone they care about more than themselves? Suppose it's not blackmail per se, but the use of the same information for more sinister threats. Does the risk of giving the FBI/others all of everyone's private data still seem acceptable?

I'm not taking a concrete position on the question, but given the secrets that plain ordinary people keep, I would not be surprised if the data available on people is used for coercion and nobody talks about it.