People cook older roosters all the time. Some people don't like them but some really enjoy the flavor. You do have to cook them long and slow with moisture. I don't know if you will enjoy them or not. Coq au Vin is a traditional recipe for old roosters. But at the very least, you can make some real good broth. You do have to have a recipe for old roosters. The recipes you find online and in most cook books assume you are using the 6 to 8 week old chicken you buy at the store and will not work.
My method for this with an old rooster is to cook him in a crock pot, usually around 10 to 12 hours. I make two batches for a large rooster but I use most body parts so it is too much for one batch. Not just the ones you normally eat but the back, neck, gizzard, heart, and feet.
To clean the feet, I scald them. The toenails twist out and the skin peels off. They wind up really clean and the feet add a lot to the broth. Not everybody uses them though. Totally up to you.
I put in a quartered onion, rough chopped celery and carrots, a bay leaf, about 10 to 15 peppercorns, and some herbs, depending on what I have around, practically always basil and oregano, sometimes parsley, chives, or thyme. Put the meat with the bones in, fill the crock pot with water to the top making sure everything is covered, and cook on low for 10 to 12 hours.
The thighs, breasts, and wishbone come out in one piece, but the drumsticks can be cooked of the bone a bit. Be careful with then or they might fall apart. These are served as the meat for a meal or two. The rest of the meat just might be cooked off the bone.
I take out what I can with a slotted spoon and separate the major pieces, them pick the meat that has cooked off the bone or pick the other bones to get shredded cooked meat that can be used in casseroles, tacos, or salads. I discard the veggies and bones. I let the broth cool enough to run it through one of those fat separators to get the fat off, then strain it through a colander with six or seven layers of cheesecloth get the bits out.
I usually end up with a little over 5 pints per crock pot cooking, or 10 to 11 pints per old rooster. What you get and how much you can cook at a time will of course depend on the size of your crock pot. You can cook them in a big pot on top of the stove or even cook them in the oven if you have the pots and pans for that. Just cook them real long and slow, just a simmer on top of the stove, not a full boil. Especially with an old rooster, that broth will often set up as a solid gelatin when you refrigerate it. I save all my carcasses, even with the young birds and make three batches at a time, then can about 16 pints of broth. I’ve never frozen the broth, but I’d imagine you could to save it. Maybe use an ice tray to get cubes so you can use only as much as you need or freeze measured amounts.
You can try brining the meat if you wish. Just soak them in salt water for a few days in the fridge before you eat them or freeze them. I usually don't brine them, just freeze them fresh and then let them thaw in the fridge for about three days before I cook them. This sort of ages them.