Trade-in has nothing to do with Applecare+. AC+ is an extended and expanded warranty service, trade-in is getting value for your old phone to put towards a new one - which model is up to you and you pay the difference.
If you have a better condition phone due to recent replacement, you might get a better trade in value but probably equals out with deductible.
It’s more the quality of the cable really, common fault is internal breakage for example because they use less and poorer quality wire. I’ve rarely had any third party fail due but I buy decent branded but inexpensive ones. I’ve not had an Apple cable fail either, but have had cosmetic damage like a lot of people where the sheathing breaks off etc.