I mention on Votaries that Major Frank Burns had more potential than the writers allowed for.
Apparently, Loretta Swit objected to her character's ongoing affair with Frank. (Maybe Swit did; maybe she didn't--what gets reported isn't always accurate).
In any case, I've always considered Major Houlihan one of the great female characters of the 1970s. She doesn't spout off the correct-sounding stuff. She is a full character with layers. And I never had any trouble understanding why the seemingly tough and ambitious Houlihan would have an affair with Frank.
First, she likely isn't as interested in marriage as she thinks she should be--she is a product of her time period, and a woman in the military is still an outlier. She sees friends getting married and settling down and having kids. She would hate that life, but a part of her thinks she is supposed to love it--until an actual marriage fails her.
Second, a person can be savvy and hard-headed in one area yet a fool with romance. She marries a jerk--in fact, she acknowledges at one point that Frank was better than her cheating husband, Lt. Colonel Penobscott, who was entirely shallow and fell short of Frank's devotion.
Third, she isn't stupid--the obvious person for her to hook up with his Hawkeye...and they would kill each other in a fortnight (as the episode when they sleep together proves). Hawkeye is too cynical. He is also, work-wise, her mirror. She doesn't need a mirror, and Hawkeye isn't comfortable with one (as the episode with a female surgeon proves).
Fourth, Houlihan has enough self-knowledge to understand herself regarding Frank. To him, she states, "You were military issue. I got you with my mess kit and khaki girdle."
Consequently, I wouldn't pair Frank with Houlihan in the long run. I would have them become good friends who can confide in each other. But Frank is looking for a wife--and, as stated above, Houlihan isn't necessarily looking for a husband, even if she thinks she is.
The above analysis is based on the character--what she does, what she says, how she says it. The complexity and strength is there!
Fantastic character! And excellently acted!