Caponization is supposed to occur no later than 5 wks old, so that the incision stays small and the testes are very small and can be removed completely and quickly during the incision. It must be performed before the animal matures in order to prevent male behaviors. Anesthesia is not used because it's very hard to calculate for individual birds (presents more of a risk of killing the bird than the surgery does). Done properly by someone who knows what they're doing, the procedure takes a couple minutes. It heals within a week or so if I recall correctly. A one year old rooster has testes that are approximately 1.5-2" long and 3/4"-1" wide, shaped like a kidney bean, and at least half an inch thick. I don't even want to imagine the incision through the breast of the bird that would be needed to remove both testes of that size, another reason they do the caponization while the birds are small.
Caponization is meant to allow a bird that is headed to the dinner table to grow larger, for longer than 16-20 weeks, while still having tender meat when processed, and also allows more flexibility in processing timeline. It was a valued and useful skill when the commercial chicken industry was in its infancy and the cornish cross did not exist. Nowadays, homesteaders may need this skill in order to produce a larger bird for the table, without relying on commercial chicken growers for chicks (which is what happens with cornish cross). But many folks get along just fine by growing out their roosters to 16-20 weeks only, or processing year old roosters via pressure cooker.
Caponizing cockerels to make pets out of them? Doesn't seem right to me. If you want a pet chicken that doesn't crow, I'd suggest getting a hen. But that's my opinion.
