>Write everything twice quickly becomes write everything 4 times once a new change appears, just as quickly as it becomes write everything 8 times, and so on.

That's a good problem to have. Getting to 4 or 8 or 12, and then pruning it to 1 or maybe 2 or 3 clearly different cases, is better than shoehorning multiple cases into the wrong abstraction, having everything that speaks with them coupled to that and dancing around their assumptions, and then having to untangle that.

Duplicated code is by definition LESS coupled.