My vibe from Claire's character development was that they tried to depict her as more of a Cersei Lannister than Hillary Clinton this season. Meaning, she may be interested in power but she's not competent enough for a leadership role. That's not to say she's completely incompetent, as she ran her own successful nonprofit with little issue.
My vibe from her was that despite her fuckups and the sacrifices she made in order to further Frank's career, she at least thought she was a partner in her relationship and Frank's reaction made her realize that she wasn't. Which is why she left.
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Frank pissing on things and breaking statues seemed like a bit much, especially after the first time it happened.
Unrelated but I didn't like Gavin's storyline this season, I'm hoping it improves next season. He was much more interesting as a hacker and far less interesting being the FBI's/Doug's bitch.