A Dearth of Horses to Come??

This is something I've been thinking about for quite a while. See what you think of it. Here goes...

With the push now to keep people from breeding their studs and mare and so many horses going to the slaughterhouse (not in the US) or even plain putting their horses down by needle or taking them to the Big Cat place (locally in southern OR), doesn't it make sense that one of these days there will/could be too small a horse population?? Like a lot less?

Could that really happen? Would prices surge skyward due to the lack of horses? Would it go back to only the upper class could have horses? Would the quality of horses be better than now since, hopefully, most of the crummy ones would have passed on to the pasture in the sky? Would people learn anything and only breed the better ones (my answer: probably not)?

Just something I've been wondering about. Will sit back and watch.