Putting aside the issue of separate racks for milk and meat dishes and plastic versus stainless interiors, if one only had one set of dishes (I know, two sets are the norm), and your hot water temperature was set at 212 F (boiling point), why couldn’t you run the dishwasher empty and then wash the clean dishes and wind up with dishes that can be used for milk or meat?

The Magen Avraham (OC 509, 11) and others (Pri Megadim, Chatam Sofer, etc.) wrote that we have the custom not to change (by kashering, that is) milk dishes to meat or vice versa. So, even if Halachacly the dishes will be Kosher – this is something not to be done as a regular practice.