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/