Okay, I have to play devil's advocate here:
There are a lot of breeds that are now recognized by the AKC that started as cross breeds, so don't discount the Puggle as a "designer breed."
A fair amount of the AKC breeds started out as cross breeds. Take, for example, the German Wirehaired Pointer, who is listed on the AKC as a legitimate purebred. It started out as a cross between "Careful crosses of the German Pointer with many other breeds. Sources differ on the exact lineage, though the Wirehaired Griffon, Poodle-Pointer mixes, Foxhound and Bloodhound are all mentioned as possible contributors."
Food for thought, no???
Nope. Completely different scenario.
When somebody actually wants to create a new breed, such as the German Wirehaired Pointer, it is done very carefully. Your quote even says "careful crosses"
There is a plan to achieve a set goal of a dog. In the German Wirehaired Pointer, it was to create a hunting dog with a very specific purpose.
Very careful selections are made of what is to be bred to what and what is to be produced. Gene Pools are locked down. Puppies that are not a step closer to the goal are culled. In the past, this meant killed. Now, they would probably be spayed and neutered and found a good home, but taken completely out of the gene pool.
Careful, CAREFUL introductions of heavily researched dogs that can contribute to the goal are selected. The ulimate goal is to create a dog that breeds true
The Puggle and other designer dogs do absolutely none of this. There isn't a goal, there aren't plans, there aren't dogs carefully selected to contribute towards the goal. There is no standard to breed towards.
If breeders were really trying to create a Puggle breed, the following steps would need to be taken:
1) Decide what purpose the Puggle is going to serve. Is it going to be a hunting dog or is it going to be a companion dog? Will it favor the hound instincts or the companion dog instincts?
2) Decide what the Puggle is going to look like. This includes height, colors, head piece, ears, tail, top line, chest, etc.
3) Find the best Pugs and Beagles that have the most to offer towards your new breed standard.
4) Breed your first litters.
5) Keep the puppies that have the most of your goals. Cull the rest.
6) Breed these puppies together.
7) Repeat step 5 for several generations until the dogs you have breed true to your standard. It may be necessary to occasionally outcross (find a Pug or a Beagle or another dog to achieve your goal). But for the most part, in the creation of a new breed, you keep your gene pool very small so that you can control the genetic outcomes.
Once you have several generations that breed true, then you have created a new breed.
Creating a new breed does NOT involve random breeding of any Pug and Beagle without any plan of what the outcome is going to be.
That is just creating mutts that backyard breeders have conned others into paying huge amounts of money for a fancy name.