Well I HAVE shown most of mine....but I certainly don't believe a horse HAS to be shown as a prerequisite to breeding.
Any "horse person" should be able to see that a horse is a correct "quality" individual, without having to have a judges opinion. That being said....I believe breeders who don't show, SHOULD at least attend a couple of rated shows each year to see where the breed is going & if they are keeping up with their own breeding program.