Congress gave away that power long ago in favor of a whole House vote on contempt of Congress, or turning over to a Federal prosecutor.
If it could be done, it would have been done in the Bush II years when there were several Administration officials who would not testify without their own conditions.
...oh well, didn’t know that. Why bother with hearings then?
Every two years a new Congress is created. I’m not sure of the legalities, but it seems impossible that some Congress in the past could hamstring all future Congresses by nullifying an inherent power.