As you're probably well aware, play in the steering system can arise from any worn moving parts such as the ball joints on track rod ends, drag link and wear within the steering box. There are also a couple of small U/Js in the length of the steering column, although wear in those is unlikely to be that noticeable but could occur.
Worn track rod ends will require replacement and although they can be relaced successfully by counting the number of threads while removing the old ones and fitting the new ones to the exact same number of threads, there's no guarantee that the result will be accurate so a tracking check should really be carried out after replacement.
Once the wheels are properly tracked and no wear on the track rod is apparent, there is no need to recheck it if work is done on the various rods connecting the steering box to the track rod. The only things such work will affect is the centralising and steering stiffness (or slackness).
By the very nature of its use, wear in the steering box is likely to be less at either end of the worm gear than in the middle which in extreme cases could result in the steering becoming stiff towards the ends of the travel especially if all of the apparent play in the box has been adjusted out and eliminated in the middle of the travel.
The condition of the steering damper can contribute to the slackness or stiffness of the steering. In extreme cases the damper could become so ineffective that the front wheels drive as if they have a mind of their own.
Suspension ball joints such as the top and bottom knuckles and rubber bushes can also contribute to "wayward" steering. In many cases replacement of these parts can require the use of a high pressure press to push the old item out of its housing and then properly position the replacement part.