I'd think even given a 5k lb tow rating, actually towing the max load would be a chore. I've done that in an older Xterra. Not a fun trip.
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While I agree a truck should be a truck, there are many other reasons people choose a truck platform. "Trucks" like the Wrangler and say, a Tacoma TRD Pro (meager 1,100lb payload), are targeting a whole different audience than those that depend on their truck for work. Others for towing their 12k lb yacht and other toys. It's like saying a "boot should be a boot." _
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Wrangler truck will serve its purpose, but again, not on the towing/payload front.
I towed 4300lbs in a new v6 Grand Cherokee. It did fine and actually had more pulling power than my half ton due to it's 300+hp and 8 speed automatic vs. the same power in my pickup with only a 4 speed auto. The ratios on the GC work out to it using 6 gears when towing where my pickup only uses 3 and it's always in the correct rpm range making it much easier to tow with and stressing the engine less. That same drivetrain in the comparatively longer wheelbase 4 door Wrangler or truck should do even better than the GC did, so I'd have zero reservations towing with it.
In any case, 5000lbs with 1200lbs payload is cutting it close for me where the z71 isn't. But, for it to be worth me ditching my Jeep, I'd want the lockers, which don't come in the z71. I'm hoping the Wrangler pickup can do GC levels of work, which really doesn't seem very much to ask considering it has the beefier full frame, longer wheelbase and the same drivetrain and should weigh around the same. Even 5500lbs would be enough for me and most others with smaller travel trailers to be comfortably within the tow rating.
The only reason I really bring it up is I know there are a ton of travel trailers that come right in that 4000lbs-5000lbs range empty, so they would be limiting their market being much under 5500lbs. I know the GC I drove in question was bought specifically because it could tow over 5000lbs without issue. All it took to be ready to tow comfortably was a $100 brake controller (it was pre-wired so just a plug under the dash) and a $200 weight distributing hitch to level it out.
Now there is a possibility that that 5000lbs zr2 rating is without a WD hitch and it goes higher if you equip it with one. I know the GC is that way - it's rated 5000lbs without WD and 6200lbs with it. I think the GC would be scary at 5000lbs without a WD hitch, but with it it's no sweat.