There is a lot of talk lately of the purpose of a steering stabilizer and its pros and cons or its necessity. So, let's start over and set the record straight with the facts.
First off, while some use it for such, it is not a "steering stabilizer." If you have to use it to stabilize the steering, then you're using it as a Band-Aid to cover up another problem. It's a steering dampener. Its job is to absorb the shock load to the steering components. By cushioning the load to the tie-rod ends, steering knuckles, and steering box, you can greatly extend their useful life. It's just like hitting your head against an unpadded rollbar. It hurts. Do it really hard enough times and you get a concussion. Add some padding and it doesn't hurt, well not as much anyway. It works the same way with the steering components.
I hear all the time from people who added larger tires to their higher-mileage rigs and it then wanders all over the road. They added a steering "stabilizer" and it went away for a while. Figuring two is better than one, they added another one to solve the problem.
Next they place the blame on the tires. They didn't have the problem until they added the larger tires so it must be the tire's problem! There are lots of other areas that most likely should get blamed first, and then fixed or replaced. The larger tires exert more leverage, which accentuates any wear in the steering box itself or the tie-rod ends. And lest we forget, what about wear in the spring-eye bushings or trailing-arm bushings and worn or improperly adjusted wheel bearings? The more wear in these components, the more the slop in the steering.
Often when larger tires are added, some form of suspension lift also takes place. This can easily change caster, camber, and proper toe. A different offset or wider wheel can change steering scrub radius and even the camber curve on an IFS vehicle. One of the biggest culprits is lack of proper axle caster. Caster is the rearward inclination of the steering knuckle. Caster is what keeps you going down the road straight and what helps the wheels to straighten out after a turn. While improper caster doesn't directly cause a wheel-wobble situation it can greatly accentuate the problem.
I used to own an early Dodge Power Wagon WM 300. For those not familiar with the model number, it looks like some of the 1 1/4-ton military trucks of WW II. This truck had seen a hard life before I got it and it showed. I totally rebuilt all the steering and driveline components to like new. I ran a homemade suspension lift, paid particular attention to the caster angle, designed a power-steering conversion, and added 42-inch Super Swampers on homemade rims. Because everything was "tight and right," it was one-finger steering and straight and true down the road or trail without a trace of wobble. All without a so-called "steering stabilizer." Yes, I did add one later.
So the point I'm making here is that if I can do it, so can you. Don't cover up a problem that will eventually get worse with a stabilizer, but by all means add one for the dampening of shock loads.