History and experience…
History. In the early days of off road racing, they found that the bearings in the steering box would get destroyed at the end of the race. The stabilizer (actually steering damper for correct terminolegy) was imployed to take the severe impacts and cushion them before they hit the steering box.
Experience. I run one. I put a fresh one on when I put the new steering box on just for long term durability of the steering box. One day on the trail the frame mounted bracket broke. The only thing I noticed on the day of trail riding and the drive home was one thing. If I drove over a rock and caught the edge of the tire, the steering wheel wanted to kick out of my hands really fast. At first I thought I was just catching a few rocks harder then usual. But after I got home I realized that it was just that the stabilizer bracket was broken. I took it off and drove on the street for a couple of weeks. Couldn’t tell if it was there or not.
Now why are you going to install one?
Save the steering box (and maybe a few fingers) when on the trail? Then yes put one on.
Because you have a shimmy on the road? Find the right fix, not a band aid.