Shaw was usingf the play to talk about class and gender differences, especially the ways that the separation of classes affect people. This theme speaks to the philosophical underpinnings of the play and is therefore more important than the dubious romance between Henry and the woman he tries to create.
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It is not a romantic play because there is no physical or emotional relationship between Professor Higgins and Eliza. They have grown dependent upon each other, but not in a romantic way. The play is more about differences in attitude and divisions between classes.

There is much debate about morals in the play. The working class characters seem to have a better awareness and attitude towards the needs of others than do members of the upper classes.

The problem comes from the dilemma about Eliza's future. She will never marry the professor. She is supposedly his social inferior and her career options are limited by her class status.
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