I don't do warranties, which is solely a personal preference.
One thing to think about here is not IF Jeep will cover the issue, but whether they CAN cover it.
I know we are are talking about JK platform in here, but has anyone tried to get OEM parts for the TJ recently?
Maybe my experience is just bad timing with the stress of a new model year and a flooded work order factory, but... I need a Dana 30 axle housing. I got it covered by insurance, money is no object, they cut a check for a full front axle replacement, all $2300 worth.
Jeep/Mopar cannot fill this order, it's been 2 months, and every time the "expected" fulfillment date gets within the business week, they back order it for another 3 weeks. I am convinced it will never arrive or there are no plans to do so.
I am basically doing all the leg work on the repair for the shop, and have sourced my own part for 1/3 the cost. I hope it works out, but if it does, Jeep will have done me no good.
My advice, if you want it, is if a part fails early, like the A/C & Temp/Fan control knobs on the TJ, buy extra while you still can. I have 3 of them sitting with my Jeep parts to transfer to a new owner. I realize that is difficult to do with expensive drivetrain items, but for $20 parts (or less), that's worth more than someone taking a dump in a box and putting a lifetime warranty on it. If it breaks early, it will break again most likely.
Again, maybe I just had some bad luck, but the headache is still real.