Im not sure when the personality type description idea came along, but alignment has never been that.
You can be surely, meek, assertive, open, neurotic, etc... all within the same alignment. Alignment is a philosophical outlook that tells us what the ultimate ideal a character's actions lead to, and how and what they are willing to do to achieve it. Which is why factions can be given an alignment as well as individuals. It already does faction play as is.
Honestly, the real f up when it comes to alignment was the mechanical punishments for not being strict enough. Those were always bad ideas and I say this as a person who really likes alignment. It has not always been implemented well, and decades later that still has an impact on folks idea of what alignment is and what its supposed to do.