This is true. Most limited slip differentials are worn out and acting like an open differential. Generally the owners don't bother spending the money to get them rebuilt because they realize they are getting by just fine and that tires are more important. A LSD only helps with getting going, it will not help you stop any faster or go around turns any faster. The clutch packs in LSD's can wear out surprisingly fast. The ones in my F150 4X4 only lasted about 30,000 miles. And I've never had my differential flushed so all that clutch pack material is still floating around in there. I need to take care of that.
Somehow I have never experienced this. I have owned:
Auburn, 170K miles, worked fine.
VLSD, 32K miles, worked fine
Torsen, 149K miles, worked fine
ELSD, 92K, worked fine
Posi-Trac, Odometer stopped working at just under 90k miles, my mechanic rebuilt the car from the ground up, took apart the diff and discovered the clutch packs were in GREAT shape, put it back togather, and I put another hellacious 20K miles on it with a crate motor, 4.10's, and a TKO500 trans. (1988 mustang GT).
Numerous crown vics with the Posi-Trac units in them, all worked fine well past 100 and even 200K miles.
^That is the list of LSD's I have experience with, and the highest mileage on the vehicle at the time I sold it. I NEVER had ANY issues with ANY LSD units.
I'm not saying YOUR F150's didn't go out, because I wasn't there to see it. What I am saying, is that I have never had an issue with multiple types of LSD's.
The Auburn is a "cone" style LSD
The Torsen uses gears and fluid viscosity/flow differential
The VLSD is a viscous unit operated by speed differential between the two rear wheels
The Posi-Trac uses clutch packs "activated" by speed differential between the two rear wheels
The ELSD used electronically controlled clutch packs
All of them except for the ELSD in the Grand Jeep Cherokee were seamless and flawless. The Jeep, I have heard it said is due to the AWD system and not necessarily the differential, that you have shudder when parking. I don't know. The whole vehicle was crap, so I won't blame the diff itself.