A lot needs to happen for a Wrangler pickup to work.
First off, I think the Jeep Wrangler is incredibly awesome. Also, my first two cars were trucks, a 1990 Ford F-250 and a 1999 Ford Ranger. With my love for Jeeps and teenage truck nostalgia I should be all-in on a Wrangler pickup. It's not that I don't think a pickup with Jeep's off-roading spirit would be cool. Trucks designed with off-roading in mind are awesome and sell well, as the Ford Raptor proved. That being I think a Wrangler-based pickup is a bad idea for a few reasons.
The mid-size truck market has been on the rise as of recently. The Chevy Colorado and GMC Canyon have sold surprisingly well, filling the space left behind by the departed Ford Ranger. The Toyota Tacoma is going nowhere anytime soon and neither is the Nissan Frontier. Americans also love the Jeep Wrangler. It speaks to our adventurous spirit. The majority of Wrangler owners will never rip the doors and roof off to go rock crawling or off-roading, but they have the option to and that's what counts. The Wrangler is an American icon and the only thing that could kill it is if Jeep decided to make it an electric-powered three-wheeler. A Jeep pickup isn't destined to be Wrangler-based, but it makes the most sense.
If Fiat Chrysler Automobiles decides to underpin the truck using another model it'd need to spend time and cash as only the next-gen Wrangler will have a truck's traditional body-on-frame design. That might be best as the Wrangler-based Gladiator concept from 2005 (seen here) looks goofy as hell. Its boxy frame gives it an outdated look and a lack of legroom for rear passengers exposes the limitations of the model. Also, where would a Wrangler-based pickup be priced at? The MSRP of a base 2016 Rubicon is $23,495. Would a truck be cheaper, and if so would it undercut sales? Say it's priced at $25,000 or up. A full cab Tacoma starts at $24,130, the Canyon and Colorado begin at $20,000, and Nissan's offering comes in at $18,000.
In terms of doing truck stuff, the current-gen Wrangler can only tow a max of 3,500 pounds. This matches the Tacoma but is far behind the Canyon/Colorado (7,000 pounds max) and Frontier (6,500 pounds max). This could change once the new model debuts. All Wrangler trucks would come with four-wheel drive, an undeniable positive and advantage over the competition. A Wrangler truck would be fun as hell to drive and wouldn't look as bad as the Gladiator. But would it be able to perform like a mid-size truck and be priced accordingly? FCA has cash to burn now that Ferrari has been spun off and there is almost no other way for Jeep to expand its lineup. I just don't think making a (novelty) truck just to have one is a good idea.