I developed Grave's when I was about 10 years ago, when I was in uni. I was kind of freaked out, and took the RI treatment without questioning it, because it was what our college nurse recommended. I didn't even discuss it with my parents or anything first.
In retrospect, I regret taking it, at least when I did. If I had it to do over again, I'd stayed on the thyroid suppressing drug that they first put me on, and waited to see how that went. From what I've read since, there's about a 25% chance of remission, even without treatment. And if I'm going to have to take a pill every day for the rest of my life, does it matter which it is?
Of course, my main reason for this regret is the trouble I've had with my weight since then; I've gained about 90 pounds, though part of that is also due to PCOS. I can't help thinking that maybe if I'd kept my own thyroid, my overall health might be better now.