In George Bernard Shaw's 1913 play Pygmalion, Eliza ends up with Freddy. However, in the 1938 film Pygmalion, directed by Anthony Asquith and Leslie Howard, she goes back to life with Higgins. I found this change very disappointing because I do not see Freddy as a bad choice.
From a handful of scenes in which Freddy (played by David Tree) appears in the film and play, it is evident that he adores Eliza (Wendy Hiller). Several times, he is shown at Eliza's door, making an effort to see her and present her with flowers, the bouquet getting bigger each time. Each time he is sent away at Higgins' command.
Also, during Eliza's debut as a lady with Mrs. Higgins (Marie Lohr), Freddy fawns over her every word. Eliza has not learned to speak outside of common slang, but Freddy assumes she is just very hip. This is an example of his blind admiration, and it is exactly why Higgins (played by Leslie Howard) sees Freddy as a pathetic fool.
"Every girl has a right to be loved," Eliza declares to Higgins. She says this aware that Freddy will give her exactly the kind of love Higgins deprives her of. She is beginning to realize how much she needs it. She knows Freddy will compliment her with sincerity, praise her when she is worthy, and will offer her his physical affection. She values his admiration for what it is worth, and that is why she comes to his defense when Higgins insults him.
Eliza also remarks that she could make something out of Freddy-why not? Why should she not take on this sort of role, now that she has the capacity? This could be the next step for her. It might give her a sense of healthy, self-earned satisfaction. We know that Freddy will be appreciative. Eliza could very easily thrive with Freddy. She could take on a teaching career in phonetics. Then, when she wanted to start a family, she could ask for financial help from her newly well-off father.
So, if Eliza married Freddy, she would have to take on the dominant role. This may feel a bit strange, especially considering her time period, but it could work.