And how do you prove a stallion if you don't bred it, just because it has a show record doesn't necessarily mean it will throw nice foals.
That is a good observation.
You can always tell the novice breeders or non-breeders because they repeat the mantra "is he shown", or "what has he done?". The question they SHOULD be asking is "what CAN he do?" rather than what has he done.
There is an equation to breeding responsibly and sucessfully...
First, is your stallion and/or mare true to its own breeding, so it can be reasonably expected to breed true. This is why it is important to either use registered breeding stock or otherwise know the pedigree so you can determine if your breeding stock is true to its own breeding.
Second, does your stallion or mare have a natural ability to do whatever you want the product (foal) to do? If there are formal competitions for that job, and if you compete, and if the standard for success in the competitions is truly the ability of the horse and not how expensive the hat or pants you wear or how well groomed and fitted your horse is, or who you know/what circles you run in, then yes, a show record can help to determine the ability of your horse. But a show record in and of itself does not actually define the horse's ability - it merely measures it for those that want it measured. Put otherwise, Secretariat could run fast. If he had never run a race, he still could have run fast.
Third, does your stallion throw or mare produce good foals - foals that are themselves true to their breeding and have the ability desired. As you said, the only way to determine that is to breed them. Some stallions or mares have excellent pedigrees and show records but are lousy breeding stock.
The bottom line is there is nothing wrong with asking "what has he done?", but people that make breeding decisions solely on the basis of the show records of their breeding stock are making their decisions based upon one piece of a puzzle with many pieces...