They had 16,000,000 reasons to do so, plus an inside track to leadership of the new regime.
Besides, I find it plausible that native Iraqis would know how and where to find Saddam a lot more easily than American GIs, for whom the country is mainly names on a map.
No disrespect for our boys, just that the natives would have a lot easier time finding and snatching him.
GMTA.