I understand the desire to be influential and to be free to expose whatever you want about yourself, but it probably doesn't work this way. By exposing too much, you limit your status.

It certainly doesn't work that way, but I think it's not just about status. If you want to be influential (aka have power, that's different from just being high-status), you should be instrumentally rational about it, that is, evaluate whether the consequences of your actions serve your goals. In this particular case, you need to carefully manage your public persona, the image you present to the outside. This careful management is not very compatible with exposing " whatever you want about yourself".

This is actually a problem in that it's a serious disincentive for good people to get involved in high-level politics. Would you want a team of smart lawyers and investigators to go over your visible life with a fine-toothed comb looking with malice for any kind of dirt they can fling at you?