Why no eligibility hearings in the House? Because the Tea Party conservatives there refuse to be duped.
It would be like a store clerk going against the mafia, besides remember the O.J Simpson trail?
No, they don`t refuse to be duped, they just don`t want to waste time on evidence that no one can agree is evidence.
I agree with your assessment, however congressional INVESTIGATIVE hearings are designed to uncover probative evidence by putting key actors under oath with the threat of perjury and/or contempt hanging over their heads.