My wife always hated the rabbitbrush that grew all over our property in Utah. She would have torn out all of it. While I will admit that it is an invasive plant, it has benefits that she just doesn't appreciate.
Rabbitbrush blooms a gorgeous golden yellow from mid-summer to early fall, and in September it is in its glory. This plant, chrysothamnus nauseosus, was useful to the native Americans who lived out west. They made chewing gum with it, cough syrup, and yellow dye. It can also be used to make rubber but that process is not cost-effective.
In early winter it provides forage for mule deer and jackrabbits. It covers vast areas, in tandem with another western invasive plant called sagebrush. (We had that in abundance too, and I enjoyed pruning it into the shape of miniature trees.)
Our long driveway was lined in part with rabbitbrush which, after a rain, exuded a wonderfully sweet aroma. But this meant nothing to my wife! She hated the stuff because in the spring, when the once golden yellow clusters of flowers dried into hay-colored puffs of seedlings, they would get all over her clothes.
In the final analysis, I choose beauty over practicality. Just because the plant is an invasive species ought not dictate its doom, especially when it has the ability to turn an entire area bright yellow.