Short of suppressing, or killing off your immune system (which is NOT an alternative, in my book) there’s nothing at this point that they can do about the antibodies.
Part of the problem is undoubtedly due to the fact that Graves is rare. How much research money goes into rare diseases?
My own “take” on why they take out the thyroid involves this logic (which may be faulty). If the immune system is perceiving the thyroid as “alien” tissue (like in transplanted organs, etc.) and is producing antibodies to fight it, then if it is no longer there, the antibody production should go down, or disappear. There will no longer be a “trigger” for antibody production. The fallacy here may be that once the antibodies are there, they stay, but I don’t know.
The other reason that they sacrifice the thyroid is to prevent future recurrences of hyperthyroidism. Being hyperthyroid involves every other organ, cell in the body, and really isn’t good for us. So by eliminating the thyroid, we can only become hyperthyroid again if we take too much synthetic thyroid hormone, which is why we have to have blood work periodically from here on out to check it.