Funny. Masanobu Fukuoka in One Straw Revolution argues for a similar approach in orchard maintenance, if I recall correctly: allowing all sorts of plants to grow below the trees and provide ground cover.
When growing plants such as carrots, as mentioned in the parent article, the crops are competing with the weeds for space, sunlight, and nutrients. In the orchard this is not an issue, and the ground cover can be beneficial to the crop.
In carrots (which are densely planted like four rows to a bed) weeds sometimes do come up in the bed between plants. They usually aren't many because the carrot tops get so dense they smother most weeds out. You can't cultivate those weeds with a tractor (without destroying the carrots) and I don't think they have a roundup resistant carrot. So it's people walking the rows with hoes from what I've seen, or some other herbicide carrots are immune too. The device in the article might be especially good for situations like this.
Oh, absolutely. One Straw Revolution isn't a weeds-are-good book. It's a description of less intrusive methods to maintain crop health.
For rice plantations, he does try to ensure weeds don't grow. I don't remember the exact methods advocated, but I believe it was placing straw all over the ground, and for some crop he grew clover in the downtime between harvest season and growing season, I think. I don't recall too much, though.