“Seems like there should be an adoption program basically giving the horses away as long as you come pick them up.”
There is and always has been. Nobody wants them anymore.
There's a really good and entertaining documentary on Netflix called "Unbroken". Four young A&M graduates tame Mustangs and ride them from Mexico to Canada. Lots of info on wild mustangs and the BLM. I can almost guarantee you'll like it a lot.