I got a kick out of reading this thread on Reddit by CellSaga21 talking about the intricate attention to detail that the Animal Crossing developers put into the game. Specifically, while the Automatic Washer could have just been an item with a throwaway animation, they decided to create a full animation that went a complete 9 minute and 41 second cycle including pre-wash, wash cycle, and spin cycle. It’s little hidden details like this that keeps this game timeless.
The Automatic washer looks like it was inspired by compact washers that are popular throughout Japan. While they're more ubiquitous in Japan and other Asian countries where space tends to be at a premium. If you're in Japan, all the big appliance makers like Panasonic, Hitache, and Sharp make compact, energy-efficient washers.