To start an investigation, probable cause is needed. Where is the probable cause that the investigators committed crimes?
Or would you just prefer show trials by a star chamber.
We need investigations of everyone in power. Or at least everyone who is accused of anything by anyone.
The investigating bodies need to be non-partisan, not appointed by anyone holding partisan office and not consisting of any partisan office-holders. They can report their findings, regardless whether there's a criminal violation. But if they find something criminal, their report would recommend criminal prosecution.
The most important function might be the fact-finding service, giving citizens good information about irresponsible behavior of those in power, rather than determining formal guilt or innocence of individuals accused of crimes. Much corruption could be exposed even if the exact criminal acts are not determined. Such investigations would serve as a deterrent to bad behavior, plus also get needed investigations done while allowing the lawmakers to turn their attention to their proper legislative function instead of the political demagoguery.