Man with Nine Children Ordered Not to Procreate: Would it work with Horses?

Source: American Herds, from Bureau of Land Management

The Supreme Court ruled a long time ago that humans have a liberty interest in procreation.  The ruling occurred because jails were performing forced sterilization on female prisoners in the belief that being a criminal was genetically passed onto offspring.

That ruling has stood, but without any clarified parameters.  Recently a judge in Wisconsin ordered a man who fathered nine children with six different women, and was $50,000 behind in child support, to NOT procreate as a condition of his probation.
The judge reportedly began the hearing by saying he was disappointed that he wasn't allowed to order that the man be sterilized.  The condition to probation can be lifted when the man shows an ability to pay child support.

There are of course an enormous number of opinions on the case, from Constitutional issues to welfare reform to the mothers of these children to how the judge can enforce this ruling.  A funny comment to the article is a rather sarcastic retort: "I'm sure a guy who ignores court orders to do stuff [pay child support] will totally obey a court order not to do stuff [procreate]."

So how we can apply this to the equine world?!

What about the breeders who breed large quantities of foals (trying to find the next Triple Crown winning Thoroughbred), but then doesn't have the means to support all the horses? A large part of the unwanted horse issue is too many horses that aren't trained and prepared to be suitable for a happy home.

I'm not a proponent of undermining breeders' due process rights, such as laws that propose taking extreme measures to restrict the right to breed, the right to privacy, or the right to earn a living.  However, I find it interesting food for thought to consider whether the more egregious breeders could be ordered- perhaps in the name of welfare laws or by the breed association or Jockey Club- to not cause his mares to procreate so many foals per year.

What do you think of that?  
A bad solution because it would be unfair/ unlawful - or - the kind of solution that cuts through the status quo to affect a difference? (Feel free to respond to the restrictions on procreation for either the man or the horse!)