Sorry I forgot to mention that since they're doing the contraceptive program they're protected from being rounded up. So by stopping that, they'll start having babies again, and when the population goes up that will allow them to remove them.
And the "round-ups for adoptions" are one of the absolute worst things that can happen to wild horses. The rounds up themselves are a terrifying and traumatic experience in which some of them will end up dead or injured, and then once they are rounded up the majority of them don't actually get adopted, most of them go the dirty, overcrowded holding pens, where they get horrible care. Oh, and at least for a while any time they saw a horse with blue eye they would kill it right there, because there is a chance, just a chance, it could be blind. And there are plenty of blind horses who live full, happy, healthy lives.
And now thanks to the Adoption Incetive Program, where the BLM will pay you for every horse you adopt, a lot of the ones that do get adopted, are taken by people who the money, barely keep them alive for the year it takes to get the money, and then dump them at an auction, where they's a very good chance they'll go to Mexico or Canada to be slaughtered.
This is some footage from a roundup last July and stuff like happens all the time
Pretty much everything that comes out of the BLM's mouths is completely. The wild horse advocacy groups have proven their claims false repeatedly, but they still won't stop.