If you mow weeds before they go to seed then you do not transfer weed seeds all over the place
To mulch properly you have to cut as high as possible so the clipping have some where to go
If you mow high and the space between the blades of grass has clippings in it then that is almost the same as mulching a garden bed
If the weed seeds get no sun & are covered by clippings then they do not germinate particularly well .
So that only leaves broadleaf weeds and you get rid of them with a top dressing of Blood & bone with strait chook poo 50;50 dusted on top
People end up with lawns full of weed because they mow too low