When a paint baby is born, it may or may not SHOW the color gene, but it will carry it (I believe), making it possible for it to produce a colored paint. I don't think people breeding for paints, necessarily hope for a solid paint (not that they would love it any less :) ), but they may end up with one. Even if it is born solid though, it is registered a paint because it has paint lines in either mom, dad, or both. That was as simply as I could put it...:)
Also, if you breed:
Paint w/color X paint w/color, you have 75% chance of paint baby
Homozygous paint X other horse solid or colored, you have 100%
Paint w/color X other breed (not paint) 50% chance of color
Paint w/color X solid paint, 75% color.......
.....I think that is the case, but someone can correct me if I am wrong...It may be a bit more complex. :)
My best guess was that they wanted to distingush between "colored" paints and "solid" paints so they could breed for color in following generations; I.e. The foal has to have a certain amount of white to be considered a "colored" foal, otherwise it's labeled as a "breeding stock" or "solid" paint. Breeding 2 colored paints together does not guarantee a colored foal, and that solid foal has less of a chance to throw color than a colored foal.. following, or have I lost you??
Anyways, breeding stock paints can't compete in all Paint shows, as they reserve most of those for colored paints - which I think is a bit "colorist" if you ask me!
Anyways, I think that labelling "breeding stock" versus "colored" is just a way of putting a label on the horse so people will be more inclined to breed colored paints and weed out the BS ones. (BS=breeding stock.. not... you know.)
I fell in love with this one BS paint foal, he was black with 4 high white stockings and a balze - GORGEOUS - but ended up not buying him because, although he was a registered PAINT, he was registered "BREEDING STOCK" ... so not as valuable... especilly if I had kept him a stallion (which I might have.. like I said.. he was gorgeous.)
Anyways, that's my stab in the dark.
Because you can't be completely 100% sure that a horse will throw great color, so thus solids get bred, sold, showed because not all people judge a horse by it's color. There just as good as paints, and since they are just as whole of a paint as a colored one is the paint association cannot prevent them from showing so they just add solid classes in the APHA.