If you have Hashimoto's, your thyroid would have died anyway, because that's what Hashimoto's does - it produces antibodies that attack and destroy thyroid tissue. If you feel better off the medication, you're not on the right medication or combination of meds...
It sounds like your medication has never been balanced properly, if you've always had symptoms. There's a good chance you don't convert the T4 medication (Synthroid, Levothyroxine, etc) to the usable Free T3, which is needed by all the cells in the body. If that's the case, you'd need to add a T3 medication, such as Cytomel. We might be able to tell that when we see your labs, but with a TSH of 146, I'd expect, both, FT4 and FT3 to be really low.
I'm assuming the Lexapro is for depression/anxiety? Those are very common symptoms of hypothyroidism. In addition, many hypo patients are deficient in vitamin D also. Many are also deficient in B-12 and iron, as well. If possible, you should try to get vitamin B-12 and ferritin (iron storage hormone) tested.
I, totally, understand why the specialist wasn't interested in discussing thyroid removal, but if he is dismissing symptoms or refusing to answer questions, etc, then I'll have to back up and say perhaps you do need to find a different doctor. You're calling him a specialist, so he's probably an endocrinologist... not all endos are good thyroid doctors, and there are really good thyroid doctors that are not endos...
No, there isn't any benefit to having your thyroid removed, at this point. It's dead and does nothing, so it's just like it's already been removed... many of us with long standing Hashimoto's are in the same situation. I, personally, would just as soon leave mine alone as to take a chance on having the parathyroids (most of us have 4 of them), which reside directly behind the thyroid, damaged during an unnecessary surgery.
Even if it weren't completely dead, it's very rare for a thyroid to be removed just because one has Hashimoto's, unless it's swollen to the point that it's causing swallowing or other issues or if there are suspicious nodules, etc.
Were you tested for Free T4 and Free T3, along with the TSH that came back at 146? If so, what were those results, with reference ranges?
If you've been hypothyroid since you were 14, I'm assuming you've been on replacement medication since then, as well... What medication/dosage have you been on?