I also have this:
My neighbors have no dandelions or any other broad-leafed plant mixed with their turfgrass, but that's because they coat their lawns with toxic chemicals. It's their choice, and I have to hope that none of it filters into my yard. It's a pretty polarized debate, weeds vs chemicals. I stand firm against poisons and neurotoxins.
My dad has taken his side, too. "Aren't you doing to do something about those dandelions?" he asked me on his spring visit. Just to be sure that I got his point, he snarled, "They're the eyesore of the neighborhood!" (I think that the unmaintained house with peeling paint and the trash can by the front door probably qualifies for that.)
I actually like the look of my meadow-like yard, full of flowers (yes, some of them yellow dandelion flowers) and bees and other life. The dandelion flowers buzz with bees and the seeds provide food for finches and sparrows. The creeping charlie yields to footsteps with a minty aroma and hosts bees all summer long. It's also drought-tolerant, stays lower than grass between mowings, and doesn't seem to be a source of allergies, as most grasses are. White clover is the ultimate ground cover, and I am seeding more of it in my yard. Yes, that's right: I bought clover seeds. Violets, among my favorite spring flowers, are spreading in the shady areas.
Dandelions have long tap roots and this is the root of why we have them here in the U.S. They were brought by early European settlers as a food plant. Gardeners will easily understand the value of a perennial, impossibly hardy, food-producing plant! The tap root makes them highly nutritious, as the plant is able to pull nutrients from deep in the soil. I regard them as good fertilizers for the lawn, when the leaves are chopped by the lawnmower and left to compost on the yard. Clover interspersed with turf grass will also fertilize the ground: as a legume, it has the capability to fix nitrogen from the air. To read more about clover lawns (clover + turf grass), look here.
Why are these useful plants demonized and poisoned? It can't be because they are invasive. No, that applies foremost to turf grass, which I can't seem to get rid of in my vegetable or flower gardens. Its roots snake along inches below the surface and it can grow through an amazing amount of stuff: my vegetable garden paths are lined with newspaper, then cotton rags, then landscape fabric, then 2-3 inches of mulch. Unbelievably, the grass is growing through all of that.
Turf grass requires endless mowing. People fertilize and herbicide it regularly. It's not drought-tolerant and results in millions of gallons of potable water dumping every year for the sake of a green lawn (if you're watering your lawn, reconsider! It just means that it requires mowing more often!).
So the next time you see a weed in your lawn, consider whether it might actually be a more useful plant than the grass it is displacing. What are its good characteristics? Anything can be a weed in the wrong place, and some plants - such as hayfever-inducing ragweed - always are.
Eventually, I hope that we will have minimal turf grass in our yard, but it'll be a long and difficult journey. I hope to replace it with little bluestem and other prairie grasses in the dry areas, and mostly clover in the more lush areas. Vegetable and fruit plants have taken up some space, and we plan to build a chicken coop this summer. Meanwhile, I'm left with the dandelion seed heads that are a reminder of all that work to come.