Soiled insulation must be removed because the odors from animal urine never dissipate completely and will remain long after the animals have been removed. Also, disease carrying organisms trapped in the old insulation can be circulated throughout the house by the heating and A/C ducts. Animal odors left behind can also attract other wildlife to your attic or crawlspace creating the same problem you had just gotten rid of. It's simply unhealthy and not worth trying to re-use contaminated insulation.
With some types of animals a full replacement is needed. Birds and bats soil large areas with their droppings and it is advisable to reinstall the entire attic or crawlspace insulation to completely rid the area of ectoparasites and odors.