Preheat the oven to 375°F and lightly grease a 9×13-inch baking dish.
Mix the shredded chicken, cream cheese, sour cream, ½ cup of the Monterey Jack cheese, all of the cheddar cheese, garlic powder, onion powder, and salt in a large bowl, stirring until the mixture is well combined and creamy.
Drizzle approximately ¼ of the enchilada sauce in the bottom of the baking dish.
Portion the chicken mixture evenly between the tortillas, roll them tightly, and place them seam-side down in the dish.
Pour the remaining enchilada sauce over the enchiladas and top with the remaining Monterey Jack cheese.
Bake uncovered for 25 to 30 minutes, until heated through, and the cheese is melted and browning.
Let the dish rest for about 5 minutes before serving, then top with your choice of garnishes.