Some people do, some don't. The purpose of withholding feed from chickens before butcher is so they don't have anything in their digestive system if you nick an intestine or some other part. To me that's not a problem, if I nick something I just rinse well but some people get really excited that.
You don't have to, I don't.
I took this from an Oklahoma State article about finishing beef and included the link below. At the end I think what you are trying to do is increase marbling (fat) as you get a better price for marbled meat.
The goal of any growing or finishing diet is to provide ad-equate amount of crude protein (CP) and energy to achieve the desired average daily gains (ADG) and desired carcass quality. As ADG increases, crude protein requirements increase, but crude protein requirements decrease as the animal grows and gets closer to slaughter. As it gets closer to slaughter weight, fat becomes a larger part of the body weight gain and muscle becomes less of the weight gained.
https://extension.okstate.edu/fact-sheets/an-introduction-to-finishing-beef.html#:~:text=The goal of any growing or finishing diet,the animal grows and gets closer to slaughter.
I could not find anything on finishing hogs. Protein on a percentage of feed drops as pork get older. I did find some on withholding feed at the end to empty the intestines. When we raised pigs on the farm when I was growing up we fed them a lot but one of our main goals was lots of fat we could render into lard. That lard was about all the oil or fat that Mom used to cook with all year.
All that to say I'm not sure what you are trying to achieve in "finishing" chickens. Are you talking about CX or Ranger types or dual purpose? Cockerels in general are not going to have much fat anyway, you need the girls for fat. I'm not sure how much actual meat they would pack on in that last week or so if you did feed them extra, not much I'd guess.
From your shirt in your icon I assume you are in the US. I suggest you call your county extension office and chat with them about this. I think they will recommend that you don't feed them out but I've been wrong before.