Volvo had a LSD option, but it only engaged at speeds below 25mph -- above that, it was inoperative (according to the accessory brochure).
One reason that would explain this precaution is that a LSD can be dangerous in certain slippery conditions such as ice. While helpful in getting going at a low speed (by sending torque to both rear wheels regardless of whether either of them lack traction), at speed it can cause a severe spinout.
What happens is based on the concept illustrated in traction circle. This is a graph that shows the grip of a tire as a function of the horizontal (acceleration, braking, lateral grip in both directions) forces. For example, a tire can show maximal traction for acceleration, or braking, or steering in a right (or left) hand turn, aka lateral traction; but when you combine two or more forces such as braking and turning at the same time, the graph reveals that the tire suffers reduced traction in both directions. This is why FWD cars have a disadvantage over RWD in racing -- a car with front tires doing both steering and accelerating is at a disadvantage over a car that splits the work between front and rear tires, each doing only one of the two tasks.
Also, the traction circle graph also shows that a spinning tire has no lateral grip at all, an important point.
Anyway, in your Volvo at road speed, you could (given driving uphill where you have to give it more gas pedal) with a LSD find yourself getting a tire slipping on ice and find both tires starting to spin, at which time the rear tires have no lateral traction at all, and your rear fishtails. In contrast, with an open differential, one tire would spin but the other tire would not, maintaining its grip on the road and keeping your rear end in proper line.
I've seen this plenty of times on slippery (from algae) boat ramps: a truck tries to pull their boat up the ramp and one rear tire starts to slip and spins uselessly, but at least the truck stays in position.
Next incident, a similar truck with a limited slip has the same problem, only in this case both rear tires are spinning (locked together by the LSD) and the rear of the truck fishtails violently -- I once saw a truck like that nearly jackknife with the boat trailer so that they were both almost lying across the water's edge. He had to unhitch the trailer, tying it to the ramp (so it wouldn't slip back into the water), to maneuver his truck safely back in line. [of course, these two stories are no credit to their stupid drivers :-)].
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