One example is Musk Thistle. It grows extremely rapidly, reproduces at a rate that's unbelievable, and is very difficult to kill. In this heavily farmed region, a few of them growing in a roadside ditch can turn into tens/hundreds of thousands of them within a year. Not only do they outcompete just about any other plant including crops, but they have incredibly sharp barbs that injure livestock.
In publicly owned spaces or abandoned fields/lots, the county has people that searches for them and sprays them with a herbicide. If they're spotted on your private land, usually they'll notify you that you have X days to cut them down (before they flower and seed) or they'll come do it whether you want them to or not. Some counties will send a bill for this, some fund it from property taxes.
If you haven't lived in an area where they vigorously grow it sounds like a huge overreaction, but left uncontrolled because one neighbor isn't taking care of it, it can become impossible to keep it out of your yard. According to wikipedia, a single plant can produce 10,000 seeds that disperse through the wind and remain viable for decades in the soil. Even the desire to not have a painful rapidly reproducing weed in your yard aside, they can do incredible damage to cropland.
It's a shame though, it's a kinda pretty flower. Imagine a vivid pink sunflower.