Our two daughters were born in 1990 and 1992 and after the free disposables that people gave us at the showers were gone, both were cloth-diapered (home laundered). Never did dump a soiled diaper in my washer and instead rinsed those things well. It seemed that no one believed that we were going to cloth-diaper and instead of a diaper service gift certificate, they gave us disposables instead. We did use disposables on trips but we think using cloth saved us a lot of money.
My mathematically-inclined sister wanted to verify the claims that disposable diapers would save money over cloth. The source of the data she was pointed to included the cost of a brand new washer and dryer as part of the cost. Of course, those two items amounted to about 90% of the overall cost of using cloth diapers.
I doubt if the cost included the number of hours spent actually doing the washing and drying, but the cost of a set of cloth diapers + water + detergent + bleach is nothing compared to the cost of disposables.