I can see the point, but it's not a workable solution. They cannot be the sole police, judge and jury of their own or else it is a recipe for abuse and corruption.
LMBO!!! Heaven forfend!
The Privilege only extends to papers etc that are directly connected to their legislative duties. The Executive absolutely cannot be looking at legitimate working papers of a Representative. Nor can any judge authorize them to do so.
The problem was how to get to the evidence without seeing the legitimate legislative papers that were there. The officers in the "filter" team did see such papers. So Hastert does have cause to complain.
Though I don't know what else could have been done except get help from the House to conduct the search.