Doesn't that make the next serving of food taste like soap?

Not food but we definitely grew up in Australia with drinks that tasted a little of detergent from a generation of families that never had a dishwasher.

Far less common now as dishwashers became cheaper and more ubiquitous.

Worthy noting not rinsing in Australia is almost certainly a regional | family habit.

Sixty plus years here and four generations of our family and most people we know rinse off plates and glasses and vigorously dry with a fresh towel.