Just speculating, but...
I don't think it would be in our interests at all to keep it hidden if we knew he were dead. You seem to be thinking that others will say "well, Saddam's dead. America can stop now."
But our mission was never solely to kill Saddam. It was to change the regime. That goes far beyond just getting rid of Saddam.
As a matter of fact, given that the loss of Saddam will (supposedly) weaken the resolve of the Republican guard and get others to begin uprising (supposedly), I would think they would want to get that info out there.
I can't really think of a good reason the US wouldn't want to get that info out.
Further speculation: Personally, I think he's already dead and his two sons are dead. Unless we know it 100%, and by 100%, I mean 150%, we don't want to say it because to state he was dead and then have him show up alive would be a PR nightmare.