If you're in the US, dandelions are an exotic invader from Europe. Why would you want to plant them on purpose? ;-D

Eating the greens, as well as allowing the root structure to improve the soil. I also found this book at journey to forever.

Here is a link that might be useful: journey to forever

Down here people grow butterfly weed to attract aphids to their garden. Why would you want to do that? Because where there is a high population of aphids, there will soon be a population of ladybugs. The butterfly weed is so attractive to aphids, that they will ignore your other plants to go for the butterfly weed. As long as you don't spray to kill the aphids anywhere in the garden, the ladybugs will remain.

Further south in Texas orchard managers are leaving nutgrass alone. It is a weed, but it does no harm to the orchard. Rather than spending their profit on meaningless weed control, they just leave it alone and leave that money in the bank.

RJ, thanks for both links, I've downloaded the book and so far only skimmed but it makes sense. I had already thought about using red clover to improve the soil in my new garden. Not sure if I can bring myself to actually buy dandelion seed as it's rampant here but might collect seed and sow in specific areas.