NY Times has an article on increased use of cover crops by farmers to build soil, increase water retention, and reduce erosion. Author cites big farms--3K to 10K acres. The cover crops seem to be a mixture. And spring planting is really no-till, though that's not clear in the article, where no-till is rather dismissed.
I remember in Nash County, NC, I think it was during my fall visit to get oriented to ASCS field operations, the CED went out to a sawmill. They were shaving logs to make the thin wood strips used in making baskets (this was before plastics). The CED signed up a couple of the workers to cover crop practices which were cost-shared under the old Agricultural Conservation Program. Under cost-sharing ASCS would pay a part of the per-acre cost for installing the practice while the farmer paid the rest. Nixon and Earl Butz tried to kill the ACP, but eventually settled for eliminating some practices, They focused on the one which increased production, which included cover crops. Their logic was similar to Greenspan's logic in supporting deregulation in the finance industry: rational financiers wouldn't take irrational risks; Butz said rational farmers would spend their own money to install cover crops.