Although it is now more controversial, the thought in the past was that prescribing thyroid medicine in someone with a nodule might help "shrink" the nodule for cosmetic purposes, and/or provide some evidence of "appropriate responsiveness" in considering the cancer risk from a nodule.
These days, nodules that are greater than 1cm in size are evaluated for cancer potential with a fine needle aspiration instead of giving thyroid hormone to see if it shrinks, because it is clear that some cancerous nodules will "shrink" with thyroid hormone and thus the response can be decieving. If the nodule has already been biposied and found to be benign, it is still a bit controversial to prescribed thyroid hormone to shrink it because it runs the risk of raising the thyroid hormone level too high (hyeprthyroidism) with can be damaging to the bones and heart.
As you can see, there are different approaches to the problem of thyroid nodules and some of these are more "style" and less "Science" based.