I wash my face in the shower in the morning but in the evening, I wash it over the sink.
I double cleanse so apply a balm to remove make up, and remove with a wrung out flannel or cloth (minimal mess at this stage)
Then I run the tap to wet my face, apply a foaming cleanser with my hands and then rinse with my hands. This is where the mess can happen! I've been washing my face like this for years, and I'm now pretty skilled but I do sometimes get damp sleeves, and IMHO, there's not much more unpleasant than soggy pyjama or dressing gown sleeves, hence my excitement at the wrist bands!
I'm also old enough to remember the towelling wristbands of the 80s...never occurred to me to use them for this purpose though!