I know a couple of Stateside wfpers that wet the window then turn the flow off and scrub then turn it back on and rinse, like Spain etc they have real dirty sandy/salty glass.
Its worth following your idea through and perfecting it if possible, if if it can save you water it could save money from making and carrying less. A smaller tank could go a long way.
Maybe its a bit like fascia cleaning with chemicals, I was taught to start at the bottom and then rinse downwards to prevent dirt/chemical run marks.