I think its a bit along the lines of permaculture - but I still dig ground over now and again before I plant my garlic bulbs or sew some seeds in a bed and I only grow a few perennial edibles so I don't quite think I'm one of the perma crowd set yet.
What I like to do is allow my veg to self seed. My first motivation for this was to save my own seed as I became more and more of a Heritage Seed Library addict. So I like to encourage my plants to flower and seed and it makes the veg plot look beautiful! My favourites have to be the umbellifereae flowers of the parsnips, carrots and parsley. Brassica flowers can look very bold with their bright yellows.
Right now in mid June, the veg in full flower is kale, kai lan, parsnip, parsley, chives, broad beans
Since I've been letting my kales flower at abandon I've been spotting ragged jack kale sprouting up all over the place. Performing its very own crop rotation. Eventually when its self seeded enough around the plot I will dig over the bed where I've been growing the kale and grow something completely different. By then I'm sure I'll have kale growing where it wishes in different spots around the plot.
I have this idea that when a plant germinates naturally it will germinate earlier and at more optimum conditions with a longer growing season than when I deem it safe and warm enough to plant the seed direct. I first starting thinking about this when I found things germinating from seed that got into my wormery compost. When I found it particularly hard to germinate seeds I started to chuck those difficult ones in the wormery so that when I used the compost on the patch I would get seedlings springing up randomly.
There are some seeds I will always plant myself such as peas and garlic but wouldn't it be wonderful if the carrot and parsnip flowers self seed across the plot and I get some surprise roots growing in a new place. The weeding will be such an adventure of discovering new seedling gifts from my flowering veg plot.