Pyometria is an infection of the uterus. It usually occurs in older intact females. Not all older intact females will develop pyometria but there is a risk as there is an increased risk of mammary cancer. Calamber maybe you were lucky with your beagles but I had a friend who just lost a beloved dachshund bitch to a closed pyometria. He was devastated.
As far as breeding goes, many breeders will spay a bitch after her breeding days are over. Most show breeders will only breed one or two litters per bitch.
I am not a fan of juvenile spays/neuters. I firmly believe in allowing an animal to mature before neutering. I believe if you can properly contain them, there is no real need to neuter a male. But there are certain health advantages to spaying females after they have had one or two heats.