Why would Michael insist that the lake be dragged?

Why would Michael draw any attention to Fredo and the lake at all?

Fredo didn't live at the compound. Who's to say he didn't leave the compound that morning for parts unknown? Who would even miss him? Who would ask questions about the disappearance of a divorced, childless Mafioso?

Quietly settling Fredo's accounts after the murder would have been easier and more prudent than putting on a "great show" to draw attention to the fact that Fredo was last seen at Michael's house.