Farmers here in Michigan plant fields of alfalfa. It sends roots down deep -- I've read up to 20 feet. The roots bring up minerals and break up hard pan. The farmer near me grow alfalfa for 2-3 years, then rotates to corn or wheat. He cuts the alfalfa for hay for his cows. When he cuts, you'd think the plants are dead, but they come back each time. To kill it, though, he sprays glyphosate.
I planted alfalfa as a cover crop in my garden once, several years ago. Two tillings the next spring took care of most of it. I still find a few plants, and I can't pull the entire root up, it goes so deep.
I planted it on a counterscarp, and sure enough, it's holding the dirt/clay very well. I plan to leave it; I can cut it for hay for the chickens or for mulch for the garden.