I suspect that pulling bindweed actually helps it multiply. If you hear it "snap" under the soil, those white
roots are left behind and it will start again. I lift from underneath with a shovel, then lift the clump carefully, not letting any pieces of white
root stay in the the soil, and immediately put it into a garbage bag and escort it off the property.
But the easiest way is to deny a perennial greenery, and that's mow, mow, mow as low as you can go. I plant my perennials far
enough apart so the mower can get in between them. Keeping the basket on collects the bad stuff, and dry it in the sun, get rid of it. In the spring sometimes I have to mow twice a week to keep the greenery about an inch. I have a really sharp shovel that I can shove into a weed and cut it off, so I make an 18" circle around perennials and mulch that heavily, going after any new weed shoots when small.
I have a rural place where there will always be weeds, the seeds blow for miles. I mow the paths and don't try to keep them weed free, just the areas around the plants.
An important distinction: Permaculture is not the same kind of gardening as organic gardening.
Mediterranean climate hugel trenches, fabuluous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.