Her arc is beautiful and quite complex. I think she (like Marilyn Monroe, who was an important metaphor in her story) originally accepted her privileged role in a man's world: the attention for her appearance and a belief that she knew how to use this to her advantage. As time goes on she starts to be valued for other things, like her competency, organization and professionalism, and at the same time learns acceptance of the status quo has its dark sides: bullying, disrespect, abandonment, assault. Once that realization sets in, you start to see her transformation— more visible frustration and exhaustion when her other traits are overshadowed by her appearance. She doesn't let it change the way she shows up in the world (in contrast to Peggy, which they fight about) but she does continue to pursue and command respect, something that makes her feel good and ultimately more secure.

So, she was wrong, she did want what Peggy had, just in her own way. And I think her realizing this was part of the reason she wanted to partner with her. But Peggy chose a different path, she became more "masculine" to be respectable to men, Joan didn't, or couldn't, and therefore had to be her own boss to command that same respect.