Initial reaction was: "hell no", but I'm starting to have second thoughts...
Since EVERYBODY is losing his/her hair at the same time, nobody would be ridiculed/laughed at. Everybody would be too busy looking at their own mirror. People would most likely be more concerned about "what is actually happening here" rather than thinking "what is happening TO ME".
Scientists all over the world would frantically start looking for cures. With the way technology/research has been expanding lately, it seems rather unlikely they wouldn't find one. If they do, you essentially improved the life quality of millions of people.
And honestly, if they don't, I think within a year everyone would be completely used to it. At the very worst, it would take until the next generation. I can imagine a baby in 2116 watching an old movie and saying "mommy why does that man have grass on his head?"
I think the most important factor is that hair serves no real purpose, other than aesthetics. We're not hurting humanity as a species, if anything, we improve it. It brings a lot of people on an equal playing field, forcing people to find other ways to thrive over other ones, rather than just winning the genetic lottery.
Probably going to get bashed to hell for this opinion, but I think you all look at it too much from an "I'm hurting others just to make myself look better", without looking at the possible bigger picture. Or maybe I'm finding an excuse to justify a selfish decision, I don't know. I just don't buy that people would still be miserable years after things died down. We're stronger than that.