The problem (IMHO) with limited slip, is in all the systems I've seen, it works on the torque multiplication method, when one wheel slips, it multiplies the torque to the other side by binding in the diff (worm gears, or the newer grooves and gears system, etc). Usually a pre set amount of multiplication can be setup, such as 3to1, 5to1, however the worm-gears or device is setup. Awesome. But if one side has zero traction, zero times anything is....zero. No power will be sent to the other side. As the OP mentions, this can be overcome by applying brake pressure, but doing that in all situations isn't always the easy, or the best idea. You can't just brake the front axle, so you'll be binding up the whole drive-train and if your back axle for instance has full traction, your killing the power to it, while trying to get the front to stop slipping, or vise versa. So in short, if one wheel has zero traction, you have an open diff.
Limited slip is wicked when there's at least some grip available, so the torque multiplication can work. On dirt roads etc you'll likely always have some grip at one tire for it to work, on sheer ice, rocks where your tire will lift, (or in an Audi rally car, hard corning causing tire lift...not a problem in the mog
![Smile :) :)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
) ditch crossing where one tire might lift, or snow where you get high centred or spin and melt into ice, not so much. Tire lifts, or is on ice, or very slippery aggregate, you have zero power to the other side.
Modern vehicles get away with this using computerized traction control systems that are capable of braking just one axle, or, even, one wheel on some systems, using the ABS system. You can't do that on a retrofitted system. On the back axle you can use the handbrake (in the case of a RWD car) but on a 4wd, if the center isn't open, your again, binding the whole drive-train, and cutting power to the front.
I wheel a lot in snow up here, open diff's and limited slip don't cut it 20"+ of snow, locker, or nothing, pressing the brakes to transfer power to the wheel with grip when pushing drifts is not an option and that's also hard on the drivetrain. I'd rather have an open front diff and a rear full locking, so when I get to the top of the hill, I can still steer (open front) and have the rear locked to finish the hill climb. Or better yet, open diff's or limited slip for ice (highway driving, as in daily driving), full locking for icy hills, backroads, and the deep stuff (fully locking both diff's on sheer ice is....not fun).
Again, just my type of wheeling.