Related I played with washing up and putting away ingredients as I cooked. Commonly I would stir then grab 30 seconds to wash a cooking pot/throw out packaging/put away in fridge etc.
It's greatly reduced the washing pots phase which commonly includes items that seem less dishwasher friendly.
I found it easy to do for most recipies I know well.
This also makes the task easier because stuff doesn't have time set on the pots -- less scrubbing -- and by avoiding a nasty dish pile, pots stays cleaner and you don't cross contaminate.
When I googled, the consensus was to wash-as-you-go.
My interpretation is that cooking is an act of creation, and when accomplished, it's over. You don't feel like doing washing up, a non-creation act, because that energy/enthusiasm is gone.
Whereas if you wash as you go, as part of the task, it also uses the energy of creation.
So: not literally time-saving, but enthusiasm-efficiency.
I reckon it also does save time. The reason is there's plenty of "dead time" during cooking. Waiting for water to boil, sauces to reduce etc. But those periods are not long enough to do much else and your hands will generally be too dirty to do even small tasks. The best use of those little sections of time is to wash up.
It's greatly reduced the washing pots phase which commonly includes items that seem less dishwasher friendly.
I found it easy to do for most recipies I know well.