I honestly have never seen a factory installed LSD (limited Slip) in the front axle in recent vehicles. The only factory installed units close, would be the air lockers in the power wagon and rubicon, along with the CXT, and some other various vehicles. It was fairly common back in the 1-ton trucks (like in the late 60's and early 70's) to have a power lock (LSD) in front ends that were dana 70. other than that, very uncommon. It wouldnt work very well in the junk CAD design that our axles use. as was mentioned, the clutches probably would wear pre maturely. The driver side shaft is connected directly to the side gear. It has to turn. When one side gear turns, it turns the spiders and the other side gear. If the other side gear (which is where the other shaft is splined to) cannot freely rotate, or is rotating at the same speed, then the movement is transmitted to the cross shaft and then to the carrier/ring/pinion, which would then make the driveshaft spin. On our trucks, by disconnecting the passenger side axle from the pass side hub/wheel, and allowing the inner part of the shaft (from the CAD to the side gear) to rotate freeley, all the motion is then just sent to that shaft, and the carrier/ring/pinion/driveshaft stay stationary. Its a pretty poor design in my opinion.
Chrysler has called LSD's everything from Anti-spin, to sure grip. In the smaller dana units, they are usually a "track lock", made by spicer. Some of the larger danas (60 and larger) will have a power lock, which is a good unit and has a dual cross shaft design (like a GM 14-bolt, or a detroit locker) so it has 2 side gears and 4 spiders.
I personally dont like any diff with clutches. If it doesnt rachet, have a cable or switch, count me out.
--Jeff