You have a 2-year-old phone, presumably with a 2-year-old battery. Figure it'll need a battery within a year, two years at the outside. I'm presuming USA on pricing here, but it's relatively similar everywhere. I'm also presuming that you plan to keep the phone for (at least) 2 years - either personally or handing it down to a family member.
AppleCare+ for 2 year will cost you $240. A battery will be $89, so deduct that from your cost - the "Real" cost is $151. So basically, is the protection from damage and/or failure, worth $151 to you? Keep in mind that the 13 Pro doesn't have a replaceable back glass; with AC+ if the back glass gets cracked it's $29... without AC+ it's $449.
I'm not going to opine; that's a decision that you need to make.