Interesting question. Since your nick is adventuregurl, I will assume you are female. Meaning hereditary general baldness is unlikely, although possible. Alopecia is definitely associated with a low thyroid level. I suppose it could manifest as a general balding trend. So, if your problem IS caused by the thyroid issues, changing them can help.
I had a low level hypothyroid condition a couple decades back. I had some associated alopecia. But I was also undergoing an advance of male pattern baldness, so I didn't notice the alopecia until later. Then I did the Hep C regime, and that pretty much killed my thyroid.
I will share what I have learned:
* using thyroid replacements fixed my alopecia. I am still going balder and balder as I grow older due to the MPB.
Which I hate, but such is life, eh?
* the US M.D. community, in general, is quite prejudiced against dessicated thyroid products (like Armour). I can find no one to validate any scientific or even reasonably rational reason for this. It just seems to be a prejudice common to the trade. Like low-cholesterol diets were for decades, or "the vapors" were 100 years ago.
* Some people report feeling "better" using Armour. Some people report the reverse. I think I feel better with Synthroid, but it is a VERY small difference.
* Armour, in the early 2000's, had some production issues (quality and compound, apparently, although I don't know for certain. As I take a partial dose of my thyroid meds as dessicated thyroid (Armour), I do know the pill quality suffered for a few years, and some dosages were just not available at all.)
* The dosages in the various alternatives: in the US that would be Armour, Synthroid, and levothyroxin, ARE NOT equivalent. If you take 130 mcg of Synthroid, you might need 175 mcg of levo to achieve the same blood levels. This is the only generic that I have ever run into where this was true, but I am not a medical professional, so take that fwiw.
* It takes a while to "stabilize" blood values when you change dosages or thyroid med types.
A lot of that you likely already know. Sorry for that, but maybe something in there will help you.
If returning to synthroid brings your blood levels (for the various thyroid tests) closer to "normal" than where you are, I would think the alopecia would improve. If your bloods are coming back with the thyroid metrics in normal ranges while you are on the compounded t3 & 4, I would tell the endo doc to pound sand, or take a hike. If changing to Synthroid or levo improves your bloods, then, and IMO, ONLY then would the endo have a point. Ultimately, afaic, you should rely primarily on how you feel while taking whichever alternative you are taking. If you feel best on the compounded med, and your bloods are coming back good, then stick with it.
However, and this is big, having said what I have, pay attention to what the blood tests tell you. The alopecia is a very strong indication that you are in a hypothyroid state, and your bloods should not be coming back with everything in "normal" ranges. If they aren't, and you like the compounded, then why not just adjust the dosages?
Good luck!