That is what we did for years. Additionally the cast iron skillet simply sat on the stove. If it needed cleaning it would get scrubbed with the hottest water and a clean scrubbing sponge or boiling water and a quick wipe (one of my biggest uses of paper towels).
For the past four years we haven’t had a dishwasher. Before that we had kids. Now we are empty nesters. Will we use the dishwasher when we move back in a month?