Batteries are generally a cheap fix from third party stores. If you wanted to keep the phone why not spend the small dollars and just replace the battery?
Indeed, even directly from Apple a new battery is a whole lot less expensive than getting another phone.
Because you need to bring it to a shop, sometimes they may keep it for more times, sometimes if they are not that honest they will find something else and factory reset it and a long etc. If it's something one can do at home by one self as an expected and supported by the vendor operation, why not? You can still bring it to a store if you don't feel like crafty enough to do it.