I am going slightly off-topic but I think this is still relevant.
If you grow something on land and then remove the resulting plant crop, the fertility of the soil is reduced.
If you use a mulching lawnmower (on your lawn, obviously) the cuttings are returned to the soil and you don't need to add fertilizer to keep the lawn healthy.
If you want a good field of strong weed free grass, cutting and removing the cuttings will take away fertility and while some strains of grass (the shorter tougher varieties) will still grow well, the weeds will die out.
Compost produced from grass cuttings (mixed with straw, leaves, old newspaper) will contain the fertility and will help new plants if used as part of their seed bed or as a mulch.
Grass cuttings on their own usually produce a squelchy smelly compost because they are too green and fertile, hence the need for dry straw-like material added to the mixture.
However, if you want to produce good hay or silage, you will need to fertilize and then (later) lime the field to keep it producing a good hay crop.
Frequent cutting or letting animals keep the grass short produces the best grass. When I was young, I lived near Dunstable Downs and there were lots of bunnies living there. They kept the grass short and it was a wonderful mixture of short springy turf and little hardy wild flowering plants. When the bunnies went (mixxy) the grass became long and rank - little use to anyone or anything. Bear in mind that chalk downland is very low on fertility as the soil is thin and drains very quickly taking any fertilizer away.