The last time I sold my phone with a year of Applecare still left on it I contacted Apple and they refunded the unused portion. My phone has been replaced a couple of times. Other than the problem of scheduling an appointment with the genius bar I just walked in and they replaced my phone with an exact duplicate. I don't think this will work if you have to have a repair or replacement phone. As I recollect the replacement cost was listed as $250, which would wipe out any Applecare credit.
As for insurance AT&T would charge me $8 a month for my 7+ 256 GB with a $299 deductible. With a $969 list price that means you would recover $670 if you have a total loss. If you lost two phones in 1 year the numbers get worse. With a total device value of $1938, they would only replace $1500 of that. This might not be an issue, of course, if your phone has a lower list price. Screen repair is only done in select locations, with a declining deductible, whatever that means.
The replacement may be "certified like-new", or other models of like kind and quality. Colors, features aren't guaranteed.
That means you have to trust AT&T a lot. Maybe folks who have had replacements can comment on their experiences.
Applecare covers an "accident from handling that is the result of an unexpected and unintentional external event (e.g. drops and damage caused by liquid contact) that arises from your normal daily usage of the Covered Device as intended for such Covered Device". It does not cover theft, wear & tear, cosmetic damage, etc. Service fee is $29 for a screen or $99 for the phone. The contract is much simpler, with less "gotchas" than the AT&T contract. But your carrier's contract might be different.
So it boils down to your own personal concerns. If you tend to loose things a lot or theft is a real concern then what do you calculate to be the odds of it happening in a year? 90%? 50%? With high numbers a full replacement contract might be useful. If your estimate is 10% or less then a contract likely would not be worth it.
Since I am relatively careful for me Applecare has met all my needs, and you get free technical support. A full replacement contract would be just throwing away money.
I would recommend a good screen protector and case though. If you are selling the phone you want the screen to be as good as new. I have dropped my phone multiple times, and luckily it has hit on the edge of my Apple case so there has never been any damage. The phones are rather robust, but if it drops on the edge of the table hitting the the screen ....