Dishwashers are commonly referred to as "dishwashers" because they perform the primary function of washing dishes. While they may not wash dishes in the same way that you would by hand, they use a combination of water, detergent, and mechanical action to clean and remove food particles, stains, and bacteria from dishes.
The term "dish sanitizer" would not accurately capture the full range of functions performed by a dishwasher. Dishwashers not only sanitize dishes by using high-temperature water and/or sanitizing cycles, but they also scrub, rinse, and dry the dishes. They are designed to provide a complete cleaning and sanitizing process in a more efficient and convenient manner than handwashing.
Furthermore, the term "dishwasher" has been in use for a long time and has become the accepted and widely recognized term for these appliances. It conveys the idea that the machine is capable of washing dishes, even though the process differs from manual washing.