Reminds me of that story about the casting of Patrick Stewart as Picard. Apparently Roddenberry originally had in mind a youthful, virogous figure much like William Shatner was for Kirk. So Stewart auditioned in a toupee to compensate for his baldness. An impressed Roddenberry realised that the toupee was pointless. Later when a reporter asked him why baldness hadn't been cured by the 24th Century, he said that society would be so advanced that no one would care anymore.
As long as you can pay for it. Not everybody can drive Ferrari. (Or rephrasing a USSR movie quote - A society without an upper/lower differentiator has no purpose)
It's complicated. The most compelling theory is that several genes might have a bit of an influence paired with the hormonal conditions in the womb. Here's an overview: