I leave some of the plant remains in place. I feel that this helps to structure the soil if roots are left in place to degrade naturally. Large plants like cabbage I chop off and take to the
compost pile but their tough roots stay in place, same with sunflowers.. If the roots happen to come out I just sliver the soil with the shovel and push the root in and cover. Over the winter they degrade quite a bit but I still have to plant next to them not on top of them... so my rows are always shifting.
After doing layered
gardening or also called
lasagna gardening Ive realized that dead plants feed the soil no matter what. My beds are hugely rich from this techniqe. Its really like a mini form of hugelhulter in my mind and the beds hold
water pretty good.... more recently I've started burying larger sticks, as it is too late to get logs in there. I've also added homemade
biochar.
I also dont compost my household scraps as I hate the mess and the flies it attracks. I just take them to the garden and bury them under 3 to 5 inches of soil in areas right in the garden next to plants. I've not seen any harm in this.