I've wondered that myself before, easy. The old superstition was that once they get a root they're no longer interested in racing. I think that's all it is. Found this article about a bloke in the US successfully combining stud duties and racing with a harness racing stallion:
http://www.thoroughbreddailynews.com/double-duty-impossible-for-stallions-think-twice-shared-archive/
http://www.thoroughbreddailynews.com/double-duty-impossible-for-stallions-think-twice-shared-archive/
Father Patrick’s experiment begs the question of whether anything other than tradition keeps Thoroughbred stallions from performing double duty.
“That’s a really good question. I’ve never been asked the question why the Thoroughbred industry doesn’t do more of that,” said Donato Lanni, director of bloodstock services for Hill ‘n’ Dale in Lexington. “I think it comes down to economics, like it always does in the Thoroughbred industry. Is it worth putting your stallion in danger of getting injured?”