Often their 'bishonen' quality is what adds to their mystery and mysticism, making them an encompassing character.
Yet at the same time they are aware of their beauty and use it as a weapon to deceive their enemies. No wonder samurais in ancient Japan wore lipstick and makeup to stun the enemy.
But bishonen is a term applied to those characters under 18. For a beautiful male character in his twenties or thirties (Aizen is seemingly in that age group??), the correct term would be 'bidanshi', meaning 'handsome man'.
Another classic example of a 'bishonen' character would be Shun from Saint Seiya:
(nosebleeds!)
Despite people understimating him during the course of the whole series, Shun proved that he was worthy of being an Athena Saint, if not one of the strongest around, just that he doesn't really like to fight.
Given the influence of the androgynous looks from Glam rock bands of the 70's and the 80's, the 'bishonen' archetype was consolidated as a pretty guy with long hair, big eyes of an unusual color, a slender, skinny physique, and feminine features, of course.
This is further proved in the Kurama character from Yu Yu Hakusho.
Bishonen characters are never afraid of being who they are, but rather embrace it, as they are basically males who embrace their feminine side, and in contrast it makes their masculinity stand out more, in my opinion.