What is the best dishwasher that doesn’t need to be taken apart to clean? 

So European style Dishwasher Miele Bosch etc all have removable  washable filters that require routine cleaning as they have no real food disposal system built in. Even some american ones have those to but the European ones definitely have more parts that are breakable on them. While all dishwashers need some sorts of maintenance I am a Kitchen Aid  guy here. The 404 604 704 series have virtually a maintenance free filtration system. You literally do nothing unless you may break a glass. Normal routine maintenance of running some cleaning solution or vinegar through them will keep the pump and wash arm free of small particles for many years!

great article on it here  KA DW Filter