It is, if anything, anti-functional: unless it smothers everything the litter provides nitrogen and nutrients as it decomposes.

Getting rid of all the litter for that “perfect lawn” requires re-introducing nitrogen artificially (historically lawns would be grown with clover, the clover being a nitrogen fixer for the grass, that stopped being a thing when people started widely applying broad-leaf herbicides like 2,4D, the lawn industry then labelled clover a weed to make killing it a goal rather than a negative side effect).

100%, like cutting grass, all the stuff you cut and move out of your lawn is nutrients leaving your soil, do that long enough and you'll get dead soil, then you'll need to buy compost... which is made from the leaves, grass cuts and bio trash that you city charges you to collect. It's a perfect cycle really.

> the lawn industry then labelled clover a weed to make killing it a goal rather than a negative side effect

People who are into bio gardening/farming use cover crops to boost soil fertility and avoid weeds, very often clovers actually. You can even use them as cover crops while growing other things, again to compete with weeds, every know and then you cut them down, leave them on the spot, they decompose and feed your crops/earthworms

https://underwoodgardens.com/cover-crops-beat-garden-weeds/

When we bought our house about 7 years ago, the lawn was in terrible shape. I’m not a huge fan of lawns—-I’ve been slowly converting it to a garden—-but my wife likes one. Instead of going chemlawn like many of our neighbors, instead we started planting clover. This horrified my father in law, who spends inordinate amounts of time removing clover and dandelions from his lawn. Anyway, after years of planting clover and the occasional overseeding with grass seed in the fall, our lawn now looks very nice. And it stays nice even during drought (like right now). We also just mulch all the fallen leaves with a mulching blade on our lawnmower. So much easier than picking up the leaves, and you can barely tell that I did not rake them. Admittedly the lawn is not 100% grass, but who cares? This is not a golf course.

Before the spread of broad-leaf herbicides and fertilisers it was just normal, you’d get clover mix at the grower or lawn care shop or your lawn seeds would come with some amount of clover mixed in.

And how much is to make it look like work, blowing that single leaf up and down the driveway is fooling no one.

Looking nice is part of the function

That doesn't sound like a garden to me, a garden produces food.