(No idea whether you'll read this, but...)
> I know you're trying to come at this from a "things could be worse" perspective
Nope, not really, I get that it matters, and how it matters.
I have two related points:
1) It matters, but it definitely doesn't matter to the magnitude that you think it does, right now - it's just one of many factors that matter. Yep, you've lost this one, so rely on your other good areas and if it helps your mindset, find some others to optimise instead. (Like, lose weight, or get ripped, get a better tan, etc.)
2) More importantly, though, your response to losing your hair is self-sabotaging: by taking it so badly, and so obviously losing confidence as a result, you're massively exacerbating the effect. Your response to your hair-loss is what is causing "...pretty much social suicide" - not the hair loss itself.
One day, I suspect you'll come through how you're currently feeling (with or without therapy?) and you'll probably have forgotten this exchange, but you'll see I'm right. But given the fickle nature of confidence, I totally get that you can't believe that right now.
PS read The Game [0] - not for the PUA nonsense, but for Neil Strauss' account of losing his hair, and how his mentality changed about it over time.
--
(Also, as an aside, I really like your concept of 'pretty privilege'. My GF is a lot more attractive, and also a lot more immediately engaging, than me; it's been enlightening to watch how different her experience of the world is, to mine.)
[0] https://www.amazon.com/dp/0060554738