I understand the appeal of just leaving weeds where they are pulled or chopping up plant leftovers and laying them on the soil, vs maintaining a compost pile.
But I have to wonder... if you look up almost any plant pest or pathogen, it says "overwinters in garden debris."
squash bugs: Squash bugs will often be found feeding on old fruit or in abandoned plantings, so clean cultivation is essential to reduce the overwintering population. https://entnemdept.ufl.edu/creatures/veg/leaf/squash_bug.htm
weevils: In the fall, adult weevils migrate to shore where
they overwinter in the leaf litter. https://www.apms.org/japm/vol39/v39p63.pdf
A fall cleanup of the yard and garden removes plant refuse on which many plant disease organisms (called pathogens) survive the winter. ... these old vegetable plants and weeds harbor diseases and insects. After a killing frost, make a total cleanup of all plants still in the garden. Take special care to remove all tomato and potato vines as well as fruits and tubers; all parts harbor blights that may cause severe losses. Be sure to remove all vines and fruits of cucumber, melon, and squash. Continue control of the cucumber beetle (Figure 1) into fall, as the bacterial wilt pathogen overwinters only in the cucumber beetle. If corn smut was a problem, destroy (by burning, burying or depositing in a sanitary landfill) all smut galls to reduce the amount of overwintering smut. https://www.ag.ndsu.edu/pubs/plantsci/hortcrop/pp737w.htm
and on and on.. I have seen MANY times that leaving plant debris, leaf litter, etc, provides overwintering spots for many pest insects and diseases.
That is one of the things that keeps me cleaning up the yard and taking it to the compost pile.
I also think that compost is a different product than broken down weeds or plant remains. Compost is created from a blend of many different items ("no more than 10% any one thing"), including carboniferous, nitrogenous, calcareous, etc etc. Greens and browns, kitchen scraps, and every conceivable macro and micro nutrient, all blended together, so that the finished product has all of that in it. It has the tilth and moisture holding capacity of humus. I prefer to add that finished product to my soil.