Thyroid meds have a pretty short half life, thats why they are taken daily.
The process of taking thyroxins is that when you start taking them your thyroid is producing thyroxins, add in exogenous thyroxins and now you have too much, the thyroid will scale back its natural production so that the body has what it thinks is the right amount of its own and externally introduced.
The problem is this process can take quite some time because the externally introduced thyroinxs can take time to hinder natural production so it becomes a game (for the docs) of wait, monitor and adjust dose but this can be a horrible experience for the patient and is often worse than the symptoms that caused them to seek help in the first place.....it can also take MONTHS to get dialed in and MANY lab tests. This all takes a lot of time and money!
If one were to give Iodine the same 6 months they would likely be much better off in the same amount of time with less sides along the way.