I think there might be different reasons for this.
First, historical reasons
The first systems with haptic feedback were mechanical systems to which vibration / force feedback functions were added (vibrations in a pilot's handle, for instance). In the early stages robotic systems were used as haptic displays for different uses (quite early, force feedback was used in telemanipulation devices for operating in nuclear power plants for instance). Naturally, the linkage-based systems became the norm.
Second, technical reasons
I see two reasons here. The first is the fact that cables can only pull and not push. Therefore, you need redundancy to generate forces and wrenches in all directions. It can become quite cumbersome and difficult to control. Also, doubling the number of motors has a direct impact on price. The second reason is related to the workspace : the larger your workspace, the longer your cables. The longer the cables, the more flexible they get. In order to be accurate, the flexibility of those cables must be compensated for, which is not necessarily a trivial problem. This links to historical reasons, as cables that could be made in the 50's were likely less good in terms of stiffness and elasticity than the ones we can make now.
All in all
I think that linkage-based systems are easier to use and to place in an experimental setup (you don't need a box the size of your workspace to use them). This being reinforced by historical reasons that made the use of linkage-based systems more or less the norm. On the other hand, cable-based mechanisms have a nice future for many applications. Also, don't forget that there are alternatives to cable and linkage-based haptic devices, with magnetic-based devices for instance.