Constitutional crises (crisises?) are exciting! Every once in awhile somebody is in contempt of congress, and you hear about the Sergeant at Arms and jail cells at the Capitol. I like your suggestion of reading things into the record. I think there's a lot of epic, Hollywood-quality drama possible with three co-equal branches of government. Given the subject matter -- the alleged perpetration of crimes against humanity -- it isn't even particularly sensationalist to advocate for the use of any one of these fancy tools our branches of government never use.
Immunity is a nasty thing. If people in our government are getting caught violating the law, it sure seems like it would be a lot better for them to stand trial and be found innocent because they were found to be acting in extraordinary or emergent circumstances. That outcome seems a whole lot better than refusing to discuss things and writing blank checks of immunity.
I won't pretend like we'd ever see a head of the CIA or a President go to jail for making national security decisions.