The reason why Poodles (Standard, Mini, and Toy) are used so widely as a breed to cross other purebred dogs with, is because of their coat.
Poodles shed a great deal less than other dog breeds. This breed is often referred to as ‘hypoallergenic’. This means that people with allergies are less likely to have an allergic reaction to a Poodle.
Poodles also come in three sizes—Standard, Miniature, and Toy—which gives breeders more control over the size of the offspring. For example, it makes more sense to cross a King Charles Cavalier Spaniel with a Toy Poodle, because they're a similar size.
Finally, Poodles have a wonderful temperament, making them ideal for families with children. The Poodle is therefore the ideal breed to use in F1B and F2B dogs, so that these three desirable traits can feature alongside the traits of the other breed involved.