The reason they don't want to do it is because a) the individual officer has to be available to the ICE personnel when they come to pick up the perp. That often means the officer has to hang around the station rather than be out doing his job, or, worse, have to come in after his shift is over and b) most local officers don't view apprehending illegals as part of their job.
The Katrina syndrome. The downside of federalism is that local, state and federal people don't act as part of the same team, but as "allies." and allies find it hard to work together in war.